Tootfinder

Democrats who attack inequality do better in elections. The party should take notice
(… something to think about while we’re remembering Joe Lieberman)
https://www.theguardian.com/commentisfree/2024/mar/22/democrats-inequality-…

Democrats who attack inequality do better in elections. The party should take notice
(… something to think about while we’re remembering Joe Lieberman)
https://www.theguardian.com/commentisfree/2024/mar/22/democrats-inequality-…

Noether inequality for irregular threefolds of general type
Yong Hu, Tong Zhang
https://arxiv.org/abs/2402.17468 https://arxiv.org/pd…

Noether inequality for irregular threefolds of general type
Let $X$ be a smooth irregular $3$-fold of general type over $\mathbb{C}$. We prove that the optimal Noether inequality $$ \mathrm{vol}(X) \ge \frac{4}{3}p_g(X) $$ holds if $p_g(X) \ge 16$ or if $X$ has a Gorenstein minimal model. Moreover, when $X$ attains the equality and $p_g(X) \ge 16$, its canonical model can be explicitly described.

A geometric approach to Poincar\'e inequality and Minkowski content of separating sets
Emanuele Caputo, Nicola Cavallucci
https://arxiv.org/abs/2402.18327

A geometric approach to Poincaré inequality and Minkowski content of separating sets
The goal of this paper is to continue the study of the relation between the Poincaré inequality and the lower bounds of Minkowski content of separating sets, initiated in our previous work [Caputo, Cavallucci: Poincaré inequality and energy of separating sets, arXiv 2401.02762]. A new shorter proof is provided. An intermediate tool is the study of the lower bound of another geometric quantity, called separating ratio. The main novelty is the description of the relation between the infima of t…

Hardy type inequalities on manifolds with nonnegative Ricci curvature
Yuxin Dong, Hezi Lin, Lingen Lu
https://arxiv.org/abs/2402.17253 https://

Hardy type inequalities on manifolds with nonnegative Ricci curvature
We prove the Hardy inequality, Heisenberg-Pauli-Weyl inequality, Hardy-Sobolev inequality, and Caffarelli-Kohn-Nirenberg (CKN) inequality on manifolds with nonnegative Ricci curvature and Euclidean volume growth, of dimension n>=3.

Ministers of Germany, Brazil, South Africa and Spain: why we need a global tax on billionaires
The multidimensional character of inequality is undeniable.
Basic services such as healthcare and education are not equally available to all.
Often, this inequality of opportunity is handed down from generation to generation.
Social origins, gender, race or where people live are some of the factors that play a role in reproducing inequalities.
Furthermore, high inequa…

“How to explain their willingness to support Trump despite the risk he poses to our system of government? The answer is not rapidly changing technology, widening inequality, unsuccessful foreign policies or unrest on university campuses but something much deeper and more fundamental. It is what the Founders worried about and Abraham Lincoln warned about: a decline in what they called public virtue.”
#GiftArticle

We have a radical democracy. Will Trump voters destroy it?
The Founding Fathers feared that Americans would someday reject their many freedoms. That’s what the 2024 election is really about.

Classification Theorem For Positive Critical Points Of Sobolev Trace Inequality
Yang Zhou
https://arxiv.org/abs/2402.17602 https://ar…

Classification Theorem For Positive Critical Points Of Sobolev Trace Inequality
We consider the Euler-Lagrange equation of Sobolev trace inequality and prove several classification results. Exploiting the moving sphere method, it has been shown, when $p=2$, positive solutions of Euler-Lagrange equation of Sobolev trace inequality are classified. Since the moving sphere method strongly relies on the symmetries of the equation, in this paper we use asymptotic estimates and two important integral identities to classify positive solutions of Euler-Langrange equation of Sobolev…

A Dimca-Greuel type inequality for foliations
Arturo Fern\'andez-P\'erez, Evelia R. Garc\'ia Barroso, Nancy Saravia-Molina
https://arxiv.org/abs/2403.18654

A Dimca-Greuel type inequality for foliations
Let $\mathcal{F}$ be a holomorphic foliation at $p\in \mathbb{C}^2$, and $B$ be a separatrix of $\mathcal{F}$. We prove the following Dimca-Greuel type inequality $\frac{μ_p(\mathcal{F},B)}{τ_p(\mathcal{F},B)}<4/3$, where $μ_p(\mathcal{F},B)$ is the multiplicity of $\mathcal{F}$ along $B$ and $τ_p(\mathcal{F},B)$ is the dimension of the quotient of $\mathbb{C}[[x,y]]$ by the ideal generated by the components of any $1$-form defining $\mathcal{F}$ and any equation of $B$. As a consequence, w…

On noncommutative H\"older inequality of Sukochev and Zanin for weak Schatten class
Yi C. Huang, Sijie Luo
https://arxiv.org/abs/2403.17990 https://…

On noncommutative Hölder inequality of Sukochev and Zanin for weak Schatten class
Sukochev and Zanin resolved an open problem due to B. Simon concerning optimal constants in Hölder inequality for the weak Schatten classes of compact operators. In this note we observe that these constants, by introducing the modified weak Schatten quasi-norms, can be renormalised so that the original Simon's conjecture (with optimal constant 1) does hold. We also provide an unexpectedly simple proof for the modified Hölder inequality and its sharpness.

On an inequality of Lin, Kim and Hsieh and Strong Subadditivity
Eric A. Carlen, Michael P. Loss
https://arxiv.org/abs/2402.15920 https://

On an inequality of Lin, Kim and Hsieh and Strong Subadditivity
We give an elementary proof of an inequality of Lin, Kim and Hsieh that implies strong subadditivity of the non Neumann entropy.

Ministers of Germany, Brazil, South Africa and Spain: why we need a global tax on billionaires
The multidimensional character of inequality is undeniable.
Basic services such as healthcare and education are not equally available to all.
Often, this inequality of opportunity is handed down from generation to generation.
Social origins, gender, race or where people live are some of the factors that play a role in reproducing inequalities.
Furthermore, high inequa…

Well this looks bad.
It's a reboot of the 1970s TV show, which was about a decent family working hard to make their lives better in a system built on inequality.
This is...not that.
Looking at you, Executive Producer Steph Curry 😒
#tvshows #streaming

Omega Theorems for Logarithmic Derivatives of Zeta and L-functions Near the 1-line
Zhonghua Li, Shengbo Zhao
https://arxiv.org/abs/2404.17250 https://

Omega Theorems for Logarithmic Derivatives of Zeta and L-functions Near the 1-line
We establish an omega theorem for logarithmic derivative of the Riemann zeta function near the 1-line by resonance method. We show that the inequality $\left| ζ^{\prime}\left(σ_A+it\right)/ζ\left(σ_A+it\right) \right| \geqslant \left(\left(e^A-1\right)/A\right)\log_2 T + O\left(\log_2 T / \log_3 T\right)$ has a solution $t \in [T^β, T]$ for all sufficiently large $T,$ where $σ_A = 1 - A / \log_2 {T}.$Furthermore, we give a conditional lower bound for the measure of the set of $t…

On convergence of a sequence of mappings with inverse modulus inequality to a discrete mapping
E. O. Sevost'yanov, V. A. Targonskii
https://arxiv.org/abs/2404.17060

On convergence of a sequence of mappings with inverse modulus inequality to a discrete mapping
We have studied the mappings that satisfy the Poletsky-type inverse inequality in the domain of the Euclidean space. It is proved that the uniform boundary of the family of such mappings is a discrete mapping. We separately considered domains that are locally connected at their boundary and regular domains in the quasiconformal sense.

On noncommutative H\"older inequality of Sukochev and Zanin for weak Schatten class
Yi C. Huang, Sijie Luo
https://arxiv.org/abs/2403.17990 https://…

On noncommutative Hölder inequality of Sukochev and Zanin for weak Schatten class
Sukochev and Zanin resolved an open problem due to B. Simon concerning optimal constants in Hölder inequality for the weak Schatten classes of compact operators. In this note we observe that these constants, by introducing the modified weak Schatten quasi-norms, can be renormalised so that the original Simon's conjecture (with optimal constant 1) does hold. We also provide an unexpectedly simple proof for the modified Hölder inequality and its sharpness.

On an inequality of Lin, Kim and Hsieh and Strong Subadditivity
Eric A. Carlen, Michael P. Loss
https://arxiv.org/abs/2402.15920 https://

On an inequality of Lin, Kim and Hsieh and Strong Subadditivity
We give an elementary proof of an inequality of Lin, Kim and Hsieh that implies strong subadditivity of the non Neumann entropy.

Sobolev space theory for Poisson's equation in non-smooth domains via superharmonic functions and Hardy's inequality
Jinsol Seo
https://arxiv.org/abs/2403.18865

Sobolev space theory for Poisson's equation in non-smooth domains via superharmonic functions and Hardy's inequality
We introduce a general $L_p$-solvability result for the Poisson equation in non-smooth domains $Ω\subset \mathbb{R}^d$, with the zero Dirichlet boundary condition. Our sole assumption for the domain $Ω$ is the Hardy inequality: There exists a constant $N>0$ such that $$ \int_Ω\Big|\frac{f(x)}{d(x,\partialΩ)}\Big|^2\mathrm{d}\,x\leq N\int_Ω|\nabla f|^2 \mathrm{d}\,x\quad\text{for any}\quad f\in C_c^{\infty}(Ω)\,. $$ To describe the boundary behavior of solutions in …

"After union membership peaked in the 1950s at 1/3 of the US workforce.. overall income inequality was close to its lowest level since its peak before the Great Depression, and was continuing to fall. Over the subsequent decades, union membership steadily declined, while income #inequality began to steadily rise after a trough in the 1970s. In 2022, union membership plateaued at 10%, while…

Labor Unions and the U.S. Economy
By Laura Feiveson, Deputy Assistant Secretary for MicroeconomicsToday, the Treasury Department released a first-of-its-kind report on labor unions, highlighting the evidence that unions serve to strengthen the middle class and grow the economy at large. Over the last half century, middle-class households have experienced stagnating wages, rising income volatility, and reduced intergenerational mobility, even as the economy as a whole has prospered. Unions can improve the well-being of middle-c…

Global existence and geometry of constant mass aspect function foliation in perturbed Schwarzschild spacetime
Pengyu Le
https://arxiv.org/abs/2404.17137 https://arxiv.org/pdf/2404.17137
arXiv:2404.17137v1 Announce Type: new
Abstract: The constant mass function foliation has been shown useful for studying the null Penrose inequality on a null hypersurface, because of the monotonicity formula of Hawking mass along such a foliation. In this paper, we show the global existence of the constant mass aspect function foliation on a nearly spherically symmetric incoming null hypersurface, emanating from a spacelike surface near the apparent horizon to the past null infinity in a vacuum perturbed Schwarzschild spacetime. Moreover, we study the geometry of the constant mass aspect function foliation, by comparing with the spherically symmetric foliation in the Schwarzschild spacetime. The knowledge about the geometry of the foliation is essential for investigating the perturbation of the constant mass aspect function foliation, which is the core in the application to the null Penrose inequality for a vacuum perturbed Schwarzschild spacetime.

Maybe people would be happier if we hadn’t let income inequality get out of control. https://time.com/5888024/50-trillion-income-inequality-america/

The Top 1% of Americans Have Taken $50 Trillion From the Bottom 90%—And That’s Made the U.S. Less Secure
A report shows that a $50 trillion redistribution of income to benefit the richest has made America less healthy, resilient, and secure.

Dplyr 1.1.0 changed how joins are working: #rstats

Links and the Diaconis-Graham Inequality
Christopher Cornwell, Nathan McNew
https://arxiv.org/abs/2404.16755 https://arxiv.org/pdf/24…

Links and the Diaconis-Graham Inequality
In 1977 Diaconis and Graham proved two inequalities relating different measures of disarray in permutations, and asked for a characterization of those permutations for which equality holds in one of these inequalities. Such a characterization was first given in 2013. Recently, another characterization was given by Woo, using a topological link in $\mathbb R^3$ that can be associated to the cycle diagram of a permutation. We show that Woo's characterization extends much further: for any permutat…

This https://arxiv.org/abs/2210.13781 has been replaced.
link: https://scholar.google.com/scholar?q=a

Energy Inequality in Climate Hazards: Empirical Evidence of Social and Spatial Disparities in Managed and Hazard-Induced Power Outages
The energy sector in the United States is ever more vulnerable to extreme climatic hazards, leading to multiple hazard-induced and managed power outages. Utility companies reportedly prioritize the restoration of power systems based on the number of outages and the size of affected populations. This approach fails to account for unequal impacts. Research in equitable infrastructure emphasizes that certain populations, such as lower income and racial-ethnic minority households, are disproportion…

This https://arxiv.org/abs/2303.16337 has been replaced.
initial toot: https://mastoxiv.page/@…

Counter-example to the strong inequality at initial low temperature
When a thermally isolated system performs a driving process in the quasistatic regime, its variation of average work $\langle W\rangle$ is equal to its quasistatic work $\langle W_{\rm qs}\rangle$. Even though presenting this simple definition, few attempts have been made to describe such equilibrium quantity from the fluctuation theorem point of view. In this work, based on Jarzynski's equality, four forms of such equality are deduced. To corroborate the results, a relation with the strong ine…

This https://arxiv.org/abs/2403.12074 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCY_…

Beyond Quantities: Machine Learning-based Characterization of Inequality in Infrastructure Quality Provision in Cities
The objective of this study is to characterize inequality in infrastructure quality across urban areas. While a growing of body of literature has recognized the importance of characterizing infrastructure inequality in cities and provided quantified metrics to inform urban development plans, the majority of the existing approaches focus primarily on measuring the quantity of infrastructure, assuming that more infrastructure is better. Also, the existing research focuses primarily on index-based…

A $(\phi_n, \phi)$-Poincar\'e inequality on John domain
Shangying Feng, Tian Liang
https://arxiv.org/abs/2403.17943 https://arxiv…

A $(ϕ_n, ϕ)$-Poincaré inequality on John domain
Given a bounded domain $Ω\subset {\mathbb R}^{n}$ with $n\ge2$, let $ϕ$ is a Young function satisfying the doubling condition with the constant $K_ϕ<2^{n}$. If $Ω$ is a John domain, we show that $Ω$ supports a $(ϕ_{n}, ϕ)$-Poincaré inequality. Conversely, assume additionally that $Ω$ is simply connected domain when $n=2$ or a bounded domain which is quasiconformally equivalent to some uniform domain when $n\ge3$. If $Ω$ supports a $(ϕ_n, ϕ)$-Poincaré inequality, we show that it…

Russian military uniforms reveal inequality between forces: https://benborges.xyz/2024/04/19/russian-military-uniforms.html

Why #Black South Carolinians are furious at Nikki #Haley: her campaign messaging dismisses concerns about deep-seated racial inequality.

Why Black South Carolinians are furious at Nikki Haley
Her campaign messaging dismisses concerns about deep-seated racial inequality.

America's 1% Has Taken $50 Trillion From the Bottom 90% | TIME https://time.com/5888024/50-trillion-income-inequality-america/

The Top 1% of Americans Have Taken $50 Trillion From the Bottom 90%—And That’s Made the U.S. Less Secure
A report shows that a $50 trillion redistribution of income to benefit the richest has made America less healthy, resilient, and secure.

Mil2: Efficient Cloth Simulation Using Non-distance Barriers and Subspace Reuse
Lei Lan, Zixuan Lu, Jingyi Long, Chun Yuan, Xuan Li, Xiaowei He, Huamin Wang, Chenfanfu Jiang, Yin Yang
https://arxiv.org/abs/2403.19272

Mil2: Efficient Cloth Simulation Using Non-distance Barriers and Subspace Reuse
Mil2 pushes the performance of high-resolution cloth simulation, making the simulation interactive (in milliseconds) for models with one million degrees of freedom (DOFs) while keeping every triangle untangled. The guarantee of being penetration-free is inspired by the interior-point method, which converts the inequality constraints to barrier potentials. Nevertheless, we propose a major overhaul of this modality by defining a novel and simple barrier formulation which does not depend on the di…

Sandwich Bernstein-Sato Polynomials and Bernstein's Inequality
Jack Jeffries, David Lieberman
https://arxiv.org/abs/2403.13146 https://

Sandwich Bernstein-Sato Polynomials and Bernstein's Inequality
Bernstein's inequality is a central result in the theory of $D$-modules on smooth varieties. While Bernstein's inequality fails for rings of differential operators on general singularities, recent work of Àlvarez Montaner, Hernández, Jeffries, Núñez-Betancourt, Teixeira, and Witt establishes Bernstein's inequality for invariants of finite groups in characteristic zero and certain other mild singularities in positive characteristic. Motivated by extending this result to new classes of singul…

This https://arxiv.org/abs/2305.11799 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Estimates for the lowest Neumann eigenvalues of parallelograms and domains of constant width
We prove sharp upper bounds for the first and second non-trivial eigenvalues of the Neumann Laplacian in two classes of domains: parallelograms and domains of constant width. This gives in particular a new proof of an isoperimetric inequality for parallelograms recently obtained by A. Henrot, A. Lemenant and I. Lucardesi.

This https://arxiv.org/abs/1709.05504 has been replaced.
link: https://scholar.google.com/scholar?q=a

A priori bounds for geodesic diameter. Part III. A Sobolev-Poincaré inequality and applications to a variety of geometric variational problems
Based on a novel type of Sobolev-Poincaré inequality (for generalised weakly differentiable functions on varifolds), we establish a finite upper bound of the geodesic diameter of generalised compact connected surfaces-with-boundary of arbitrary dimension in Euclidean space in terms of the mean curvatures of the surface and its boundary. Our varifold setting includes smooth immersions, surfaces with finite Willmore energy, two-convex hypersurfaces in level-set mean curvature flow, integral curr…

A $(\phi_n, \phi)$-Poincar\'e inequality on John domain
Shangying Feng, Tian Liang
https://arxiv.org/abs/2403.17943 https://arxiv…

A $(ϕ_n, ϕ)$-Poincaré inequality on John domain
Given a bounded domain $Ω\subset {\mathbb R}^{n}$ with $n\ge2$, let $ϕ$ is a Young function satisfying the doubling condition with the constant $K_ϕ<2^{n}$. If $Ω$ is a John domain, we show that $Ω$ supports a $(ϕ_{n}, ϕ)$-Poincaré inequality. Conversely, assume additionally that $Ω$ is simply connected domain when $n=2$ or a bounded domain which is quasiconformally equivalent to some uniform domain when $n\ge3$. If $Ω$ supports a $(ϕ_n, ϕ)$-Poincaré inequality, we show that it…

Revisiting Bohr Inequalities with Analytic and Harmonic Mappings on unit disk
Molla Basir Ahamed, Partha Pratim Roy
https://arxiv.org/abs/2402.15689 https:…

Revisiting Bohr Inequalities with Analytic and Harmonic Mappings on unit disk
In this paper, we study some improved and refined versions of the classical Bohr inequality applicable to the class $\mathcal{B}$, which consists of self-analytic mappings defined on the unit disk $\mathbb{D}$. First, we improve the Bohr inequality for the class $\mathcal{B}$ of analytic self-maps, incorporating the area measurements of sub-disks $\mathbb{D}_r$ of $\mathbb{D}$. Secondly, we establish a sharp inequality with suitable setting as an improved version of the classic Bohr inequality.…

Mass Concentration of Two-Spinless Fermi Systems with Attractive Interactions
Yujin Guo, Yan Li
https://arxiv.org/abs/2403.17591 https://

Mass Concentration of Two-Spinless Fermi Systems with Attractive Interactions
We study the two-spinless mass-critical Fermi systems with attractive interactions and trapping potentials. We prove that ground states of the system exist, if and only if the strength $a$ of attractive interactions satisfies $0

Found my new shirt...
➡️ https://cottonbureau.com/p/H2M4SD/shirt/eat-the-rich#/18416258/tee-men-standard-tee-premium-heather-tri-blend-xl

Eat the Rich by Resistbot
Yum! Show your distaste for grotesque wealth inequality and promote civic engagement at the same time.

Hoeffding's inequality for continuous-time Markov chains
Jinpeng Liu, Yuanyuan Liu, Lin Zhou
https://arxiv.org/abs/2404.14888 https://

Hoeffding's inequality for continuous-time Markov chains
Hoeffding's inequality is a fundamental tool widely applied in probability theory, statistics, and machine learning. In this paper, we establish Hoeffding's inequalities specifically tailored for an irreducible and positive recurrent continuous-time Markov chain (CTMC) on a countable state space with the invariant probability distribution $π$ and an $\mathcal{L}^{2}(π)$-spectral gap $λ(Q)$. More precisely, for a function $g:E\to [a,b]$ with a mean $π(g)$, and given $t,\varepsilon>0$, we der…

This https://arxiv.org/abs/2402.18966 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Vector Valued Gårding Inequality for pseudo-differential operators on compact homogeneous manifolds
We prove sufficient conditions in order to obtain a sharp Gårding inequality for pseudo-differential operators acting on vector-valued functions on compact Lie groups. As a consequence, we obtain a sharp Gårding inequality for compact homogeneous vector bundles and compact homogeneous manifolds. The sharp Gårding inequality is the strongest lower bound estimate known to hold for systems on $\mathbb{R}^n$, and the aim of this paper is to extend this property to systems on compact Lie groups a…

This https://arxiv.org/abs/2311.03197 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_ees…

Stable Linear Subspace Identification: A Machine Learning Approach
Machine Learning (ML) and linear System Identification (SI) have been historically developed independently. In this paper, we leverage well-established ML tools - especially the automatic differentiation framework - to introduce SIMBa, a family of discrete linear multi-step-ahead state-space SI methods using backpropagation. SIMBa relies on a novel Linear-Matrix-Inequality-based free parametrization of Schur matrices to ensure the stability of the identified model. We show how SIMBa generally…

How might we address this problem?
#IncomeInequality vs

Why the world cannot afford the rich
Equality is essential for sustainability. The science is clear — people in more-equal societies are more trusting and more likely to protect the environment than are those in unequal, consumer-driven ones.

How might we address this problem?
#IncomeInequality vs

Why the world cannot afford the rich
Equality is essential for sustainability. The science is clear — people in more-equal societies are more trusting and more likely to protect the environment than are those in unequal, consumer-driven ones.

"When [we] dreamed up the #SciFiEconomics Lab(2019) we had no idea what #Graeber & Wengrow were up to. Yet, like them, we felt stuck. We felt crippled by our inability to imagine living under any system other than late-stage

What David Graeber and David Wengrow's "The Dawn of Everything" has in common with sci-fi economics
Photo: Dennis Jarvis CC-BY – link A few weeks ago, I finished David Graeber and David Wengrow’s The Dawn of Everything. It is not science fiction, nor is it economics. And yet, I propose it has to do with both. The book begins by stating inequality has risen to the top of the agenda for public debate. Scholars, politicians, business leaders are calling attention to it. Where, they ask, does inequality come from? How can we reduce it to tolerable levels? The authors then proceed to questio…

This https://arxiv.org/abs/2002.00914 has been replaced.
link: https://scholar.google.com/scholar?q=a

The relative isoperimetric inequality for minimal submanifolds with free boundary in the Euclidean space
In this paper, we mainly consider the relative isoperimetric inequalities for minimal submanifolds with free boundary. We first generalize ideas of restricted normal cones introduced by Choe-Ghomi-Ritoré in \cite{CGR06} and obtain an optimal area estimate for generalized restricted normal cones. This area estimate, together with the ABP method of Cabré in \cite{Cabre2008}, provides a new proof of the relative isoperimetric inequality obtained by Choe-Ghomi-Ritoré in \cite{CGR07}. Furthermore…

This https://arxiv.org/abs/2403.10564 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

All incompatible measurements on qubits lead to multiparticle Bell nonlocality
Bell nonlocality is a fundamental phenomenon of quantum physics as well as an essential resource for various tasks in quantum information processing. It is known that for the observation of nonlocality the measurements on a quantum system have to be incompatible, but the question which incompatible measurements are useful, remained open. Here we prove that any set of incompatible measurements on qubits leads to a violation of a suitable Bell inequality in a multiparticle scenario, where all par…

$l^2$ decoupling theorem for surfaces in $\mathbb{R}^3$
Larry Guth, Dominique Maldague, Changkeun Oh
https://arxiv.org/abs/2403.18431 https://

$l^2$ decoupling theorem for surfaces in $\mathbb{R}^3$
We identify a new way to divide the $δ$-neighborhood of surfaces $\mathcal{M}\subset\mathbb{R}^3$ into a finitely-overlapping collection of rectangular boxes $S$. We obtain a sharp $(l^2,L^p)$ decoupling estimate using this decomposition, for the sharp range of exponents $2\leq p\leq 4$. Our decoupling inequality leads to new exponential sum estimates where the frequencies lie on surfaces which do not contain a line.

Quote:"Without an analysis of power, it is hard to understand inequality or much else in modern capitalism."
Good that finally some economists are waking up to see how much their simplistic models have ruined the world.
(Original title: Nobel laureate economist savages profession as clueless, unethical)

Nobel laureate economist savages his own profession as clueless and unethical
Nobel Laureate economist Angus Deaton has delivered a ferocious rebuke to his own profession, saying economists have failed to understand that capitalism is about power.

Study of quantum non-locality by CHSH function and its extension in disordered fermions
Yoshihito Kuno
https://arxiv.org/abs/2402.17513 https://

Study of quantum non-locality by CHSH function and its extension in disordered fermions
Quantum non-locality is an important concept in quantum physics. In this work, we study the quantum non-locality in a fermion many-body system under quasi-periodic disorders. The Clauser-Horne-Shimony-Holt (CHSH) inequality is systematically investigated, which quantifies quantum non-locality between two sites. We find that the quantum non-locality explicitly characterize the extended and critical phase transitions, and further that in the globally averaged picture of maximum value of the quant…

Navigating Complexity: Constrained Portfolio Analysis in High Dimensions with Tracking Error and Weight Constraints
Mehmet Caner, Qingliang Fan, Yingying Li
https://arxiv.org/abs/2402.17523

Navigating Complexity: Constrained Portfolio Analysis in High Dimensions with Tracking Error and Weight Constraints
This paper analyzes the statistical properties of constrained portfolio formation in a high dimensional portfolio with a large number of assets. Namely, we consider portfolios with tracking error constraints, portfolios with tracking error jointly with weight (equality or inequality) restrictions, and portfolios with only weight restrictions. Tracking error is the portfolio's performance measured against a benchmark (an index usually), {\color{black}{and weight constraints refers to specific al…

I've been reading Ray Dailo's "Principles for dealing with the changing world order" in which he charts the rise and fall of empires and kingdoms and dynasties.
The main cycle, he reckons is:
1) Winner of a war consolidates power, unites the population (often through oppression)
2) A smart cooperative equitable educated society with meritocracy means good societal progress and wide sharing of the wealth.
3) Long period of peace, building good tech and military and financial systems.
4) Leadership corrupts: Excessive debt, money-printing, inequality, financial ruin, no sense of solidarity, then a natural disaster pushes it over the edge
5) The fall: Escalating rebellions, very bad inequality, internal conflicts
6) Civil war, revolution, eventually a strong leader proves the winner and back to 1.
We in the western civilization are very clearly in the late states of this kind of cycle, and it's frankly terrifying with the weapons we have these days when it comes to a war.
The leadership is too corrupt to try and fix the inequality or invest in that well educated, equitable, cooperative society.
He explicitly agrees with Marx and implicitly with me a lot more than I'd have expected from the rabid capitalist that Ray Dailo is.
It's interesting to hear his emphasis on inequality and how a prosperous society depends upon sharing the gains of prosperity widely. You tend to hear hyper-capitalists mostly emphasizing that capital's gains should go to capital, and Ray is certainly suggesting the opposite here. That if that happens, it corrupts the leadership and ends with cronyism and debt and revolution.
We seem to basically agree what creates good prosperous peaceful civil society, and that capitalism in the Anglican world isn't doing it, and that fucked up corrupt government is why we aren't doing it.
We'd offer fairly different prescriptions though I think.
#reading #books #economics

Equilibria, Efficiency, and Inequality in Network Formation for Hiring and Opportunity
Cynthia Dwork, Chris Hays, Jon Kleinberg, Manish Raghavan
https://arxiv.org/abs/2402.13841 <…

Equilibria, Efficiency, and Inequality in Network Formation for Hiring and Opportunity
Professional networks -- the social networks among people in a given line of work -- can serve as a conduit for job prospects and other opportunities. Here we propose a model for the formation of such networks and the transfer of opportunities within them. In our theoretical model, individuals strategically connect with others to maximize the probability that they receive opportunities from them. We explore how professional networks balance connectivity, where connections facilitate opportunity…

Probabilistic work extraction on a classical oscillator beyond the second law
Nicolas Barros, Sergio Ciliberto, Ludovic Bellon
https://arxiv.org/abs/2402.18556

Probabilistic work extraction on a classical oscillator beyond the second law
We demonstrate experimentally that, applying optimal protocols which drive the system between two equilibrium states characterized by a free energy difference $ΔF$, we can maximize the probability of performing the transition between the two states with a work $W$ smaller than $ΔF$. The second law holds only on average, resulting in the inequality $\langle W \rangle \geq ΔF$. The experiment is performed using an underdamped oscillator evolving in a double-well potential. We show that with a …

This https://arxiv.org/abs/2306.11131 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Delayed Gronwall inequality with weakly singular kernel
Delay Gronwall inequality with a weakly singular kernel has been a subject of interest in various mathematical studies. In this article, we will delve into the consideration of this inequality and its application in the study continuity of the state trajectory for a Volterra integral equation with delay. Using delay Gronwall inequality with a singular kernel, we investigate the behavior and properties of the state trajectory if there are delays. This analysis aims to improve our understanding o…

This https://arxiv.org/abs/2402.10299 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Stability for the 3D Riemannian Penrose inequality
We show that Schwarzschild manifold is stable for the 3-dimensional Riemannian Penrose inequality in the pointed measured Gromov-Hausdorff topology modulo negligible spikes and boundary area perturbations.

H\"ormander type Fourier multiplier theorem and Nikolskii inequality on quantum tori, and applications
Michael Ruzhansky, Serikbol Shaimardan, Kanat Tulenov
https://arxiv.org/abs/2402.17353

Hörmander type Fourier multiplier theorem and Nikolskii inequality on quantum tori, and applications
In this paper, we study Hörmander type Fourier multiplier theorem and the Nikolskii inequality on quantum tori. On the way to obtain these results, we also prove some classical inequalities such as Paley, Hausdorff-Young, Hausdorff-Young-Paley, Hardy-Littlewood, and Logarithmic Sobolev inequalities on quantum tori. As applications we establish embedding theorems between Sobolev, Besov spaces as well as embeddings between Besov and Wiener and Beurling spaces on quantum tori. We also analyse $β…

This https://arxiv.org/abs/2403.08070 has been replaced.
link: https://scholar.google.com/scholar?q=a

On the Ashbaugh-Benguria type conjecture about lower-order Neumann eigenvalues of the Witten-Laplacian
An isoperimetric inequality for lower order nonzero Neumann eigenvalues of the Witten-Laplacian on bounded domains in a Euclidean space or a hyperbolic space has been proven in this paper. About this conclusion, we would like to point out two things: It strengthens the well-known Szegő-Weinberger inequality for nonzero Neumann eigenvalues of the classical free membrane problem given in [J. Rational Mech. Anal. 3 (1954) 343-356] and [J. Rational Mech. Anal. 5 (1956) 633-636]; Recently, Xia-…

Interessant artikel over ongelijkheid in Nature.
#nature

Why the world cannot afford the rich
Equality is essential for sustainability. The science is clear — people in more-equal societies are more trusting and more likely to protect the environment than are those in unequal, consumer-driven ones.

On Littlewood's estimate for the modulus of the zeta function on the critical line
Emanuel Carneiro, Micah B. Milinovich
https://arxiv.org/abs/2403.17803

On Littlewood's estimate for the modulus of the zeta function on the critical line
Inspired by a result of Soundararajan, assuming the Riemann hypothesis (RH), we prove a new inequality for the logarithm of the modulus of the Riemann zeta-function on the critical line in terms of a Dirichlet polynomial over primes and prime powers. Our proof uses the Guinand-Weil explicit formula in conjunction with extremal one-sided bandlimited approximations for the Poisson kernel. As an application, by carefully estimating the Dirichlet polynomial, we revisit a 100-year-old estimate of Li…

This https://arxiv.org/abs/2305.01530 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On cubic-line arrangements with simple singularities
In the present note we study combinatorial and algebraic properties of cubic-line arrangements in the complex projective plane admitting nodes, ordinary triple and $A_{5}$ singular points. We deliver a Hirzebruch-type inequality for such arrangement and we study the freeness of such arrangements providing an almost complete classification.

This https://arxiv.org/abs/2311.02445 has been replaced.
initial toot: https://mastoxiv.page/@arX…

Pre-Construction of Opinion Dynamics Considering Structural Inequality: Interdisciplinary Analysis of Complex Social Stratification, Media Influence, and Functionalism
This study analyzes the role of meritocracy, media influence, and scheduled theory from multiple perspectives as mechanisms that maintain inequality in social classes. Social inequality exists in complex forms in the educational, media, and political spheres. The study focuses on how inequality in society is structured and reproduced and how the theory of scheduled harmony justifies this.

Heintze-Karcher Type Inequalities of Fractional GJMS Operators
Huihuang Zhou
https://arxiv.org/abs/2402.18160 https://arxiv.org/pdf/2…

Heintze-Karcher Type Inequalities of Fractional GJMS Operators
In this paper, we genelize the Heintze-Karcher type inequalities for fractional Q-curvature $Q_{2γ}$ on conformally compact Einstein manifolds. Such inequality holds for all $γ\in (0,1]$. In particular, for $γ=\frac{1}{2}$ and $γ=1$, we obtain some rigidity theorems by characterising the equalities. Moreover, we also verify the Heintze-Karcher inequality on Riemannian manifolds with sectional curvature bounded below.

This https://arxiv.org/abs/2403.08075 has been replaced.
link: https://scholar.google.com/scholar?q=a

Several isoperimetric inequalities of Dirichlet and Neumann eigenvalues of the Witten-Laplacian
In this paper, by mainly using the rearrangement technique and suitably constructing trial functions, under the constraint of fixed weighted volume, we can successfully obtain several isoperimetric inequalities for the first and the second Dirichlet eigenvalues, the first nonzero Neumann eigenvalue of the Witten-Laplacian on bounded domains in space forms. These spectral isoperimetric inequalities extend those classical ones (i.e. the Faber-Krahn inequality, the Hong-Krahn-Szegő inequality and…

Beyond Quantities: Machine Learning-based Characterization of Inequality in Infrastructure Quality Provision in Cities
Bo Li, Ali Mostafavi
https://arxiv.org/abs/2403.12074

Beyond Quantities: Machine Learning-based Characterization of Inequality in Infrastructure Quality Provision in Cities
The objective of this study is to characterize inequality in infrastructure quality across urban areas. While a growing of body of literature has recognized the importance of characterizing infrastructure inequality in cities and provided quantified metrics to inform urban development plans, the majority of the existing approaches focus primarily on measuring the quantity of infrastructure, assuming that more infrastructure is better. Also, the existing research focuses primarily on index-based…

Some Generalizations of Mercer inequality and its operator extensions
Mohsen Kian, Zainab Peymani Mazraj
https://arxiv.org/abs/2403.17557 https://

Some Generalizations of Mercer inequality and its operator extensions
We study the Mercer inequality and its operator extension for superquadratic functions. In particular, we give a more general form of the Mercer inequality by replacing some constants by positive operators. As some consequences, our results produce a Jensen operator inequality for superquadratic functions. Moreover, we present some Mercer inequalities of Hermite-Hadamard's type.

On several new results related to Richard's inequality
Cristian Conde, Ni\c{c}usor Minculete
https://arxiv.org/abs/2403.17559 https://

On several new results related to Richard's inequality
The main study of this article is the characterization of Richard's inequality, because it is closely related to Buzano's inequality. Finally, we present a newapproach for Richard's inequality, where we use the Selberg operator.

Navigating Complexity: Constrained Portfolio Analysis in High Dimensions with Tracking Error and Weight Constraints
Mehmet Caner, Qingliang Fan, Yingying Li
https://arxiv.org/abs/2402.17523

Navigating Complexity: Constrained Portfolio Analysis in High Dimensions with Tracking Error and Weight Constraints
This paper analyzes the statistical properties of constrained portfolio formation in a high dimensional portfolio with a large number of assets. Namely, we consider portfolios with tracking error constraints, portfolios with tracking error jointly with weight (equality or inequality) restrictions, and portfolios with only weight restrictions. Tracking error is the portfolio's performance measured against a benchmark (an index usually), {\color{black}{and weight constraints refers to specific al…

Nonequilibrium relaxation inequality on short timescales
Andrea Auconi
https://arxiv.org/abs/2403.16631 https://arxiv.org/pdf/2403.16…

Nonequilibrium relaxation inequality on short timescales
An integral relation is derived from the Fokker-Planck equation which connects the steady-state probability currents with the dynamics of relaxation on short timescales in the limit of small perturbation fields. As a consequence of this integral relation, a lower bound on the steady-state entropy production is obtained. For the particular case of an ensemble of random perturbation fields of weak spatial gradient, a simpler bound is derived from the integral relation which provides a feasible me…

This https://arxiv.org/abs/2404.09085 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On the Spectral Large Sieve Inequality for $\mathrm{PGL}_2 (\mathbb{Z}[i]) \backslash \mathrm{PGL}_2 (\mathbb{C})$
In this paper, we introduce concise expressions for the complex Bessel integral that enables us to improve the spectral large sieve inequality of Watt for $\mathrm{PGL}_2 (\mathbb{Z}[i]) \backslash \mathrm{PGL}_2 (\mathbb{C})$. Our result is optimistic in the case when the average of spectral parameters is on a square centered at $(0, 0)$.

This is in the inbox of a lot of low-income people:
“The Federal Communications Commission (FCC) has announced that the ACP is ending and April 2024 will be the last month you receive your full ACP discount.”
—
#inequality #ACP

Oppenheim-Schur's inequality and RKHS
Akira Yamada
https://arxiv.org/abs/2402.16228 https://arxiv.org/pdf/2402.16228

Oppenheim-Schur's inequality and RKHS
In 2012, we obtained Oppenheim's inequality for positive semidefinite matrices and its equality condition by the reproducing kernel method. In this paper, as a continuation, we give a reproducing kernel proof of the block matrix version of the Oppenheim-Schur's inequality and its equality condition in the positive definite case.

Rigidity of spin fill-ins with non-negative scalar curvature
Simone Cecchini, Sven Hirsch, Rudolf Zeidler
https://arxiv.org/abs/2404.17533 https://arxiv.org/pdf/2404.17533
arXiv:2404.17533v1 Announce Type: new
Abstract: We establish new mean curvature rigidity theorems of spin fill-ins with non-negative scalar curvature using two different spinorial techniques. Our results address two questions by Miao and Gromov, respectively. The first technique is based on extending boundary spinors satisfying a generalized eigenvalue equation via the Fredholm alternative for an APS boundary value problem, while the second is a comparison result in the spirit of Llarull and Lott using index theory. We also show that the latter implies a new Witten-type integral inequality for the mass of an asymptotically Schwarzschild manifold which holds even when the scalar curvature is not assumed to be non-negative.

On the existence and uniqueness of an elliptic variational inequality coupled with a nonlinear differential equation
Nadia Skoglund Taki
https://arxiv.org/abs/2402.16620

On the existence and uniqueness of an elliptic variational inequality coupled with a nonlinear differential equation
This paper deals with the existence, uniqueness, and boundedness of a solution to a general fully coupled nonlinear system of equations modelling a static frictional adhesion contact problem. The model has two unknowns; the displacement $u$ of a cylinder in contact with an obstacle, and the intensity of adhesion denoted by $β$ with range $[0,1]$. In literature, restrictions are made on the physical system forcing $β$ to stay in $[0,1]$. We relax these restrictions and show that the solution $…

This https://arxiv.org/abs/2403.06081 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A remark on the first eigenvalue of the p-Laplacian on compact submanifolds in the unit sphere
An integral inequality for the singular p-laplacian is established for 3/2

Unique continuation for a gradient inequality with $L^n$ potential
Adam Coffman, Yifei Pan, Yuan Zhang
https://arxiv.org/abs/2402.15503 https://

Unique continuation for a gradient inequality with $L^n$ potential
We establish a unique continuation property for solutions of the differential inequality $|\nabla u|\leq V|u|$, where $V$ is locally $L^n$ integrable on a domain in $\mathbb R^n$. A stronger uniqueness result is obtained if in addition the solutions are locally Lipschitz. One application is a finite order vanishing property in the $L^2$ sense for the exponential of $W^{1,n}$ functions. We further discuss related results for the Cauchy-Riemann operator $\bar\partial$ and char…

Inequality indices for heterogeneous systems: a tool for failure prediction
Tarun Ram Kanuri, Subhadeep Roy, Soumyajyoti Biswas
https://arxiv.org/abs/2402.14747

Inequality indices for heterogeneous systems: a tool for failure prediction
We have numerically studied a mean-field fiber bundle model of fracture at a non-zero temperature and acted by a constant external tensile stress. The individual fibers fail (local damage) due to creep-like dynamics that lead up to a catastrophic breakdown (global failure). We quantify the variations in sizes of the resulting avalanches by calculating the Lorenz function and two inequality indices -- Gini ($g$) and Kolkata ($k$) indices -- derived from the Lorenz function. We show that the two …

This https://arxiv.org/abs/2306.06187 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Faber-Krahn inequalities, the Alt-Caffarelli-Friedman formula, and Carleson's $\varepsilon^2$ conjecture in higher dimensions
The main aim of this article is to prove quantitative spectral inequalities for the Laplacian with Dirichlet boundary conditions. More specifically, we prove sharp quantitative stability for the Faber-Krahn inequality in terms of Newtonian capacities and Hausdorff contents of positive codimension, thus providing an answer to a question posed by De Philippis and Brasco. One of our results asserts that for any bounded domain $Ω\subset\mathbb R^n$, $n\geq3$, with Lebesgue measure equal to that …

This https://arxiv.org/abs/2312.15232 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On Harnack inequality and harmonic Schwarz lemma
In this paper, we study the $(s, C(s))$-Harnack inequality in a domain $G\subset \mathbb{R}^n$ for $s\in(0,1)$ and $C(s)\geq1$ and present a series of inequalities related to $(s, C(s))$-Harnack functions and the Harnack metric. We also investigate the behavior of the Harnack metric under $K$-quasiconformal and $K$-quasiregular mappings, where $K\geq 1$. Finally, we provide a type of harmonic Schwarz lemma and improve the Schwarz-Pick estimate for a real-valued harmonic function.

This https://arxiv.org/abs/2309.04923 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On improvements of the Hardy, Copson and Rellich inequalities
Using a method of factorization and by introducing a generalized discrete Dirichlet's Laplacian matrix $(-Δ_Λ)$, we establish an extended improved discrete Hardy's inequality and Rellich inequality in one dimension. We prove that the discrete Copson inequality (E.T. Copson, \emph{Notes on a series of positive terms}, J. London Math. Soc., 2 (1927), 9-12.) in one-dimension admits an improvement. We also prove that the improved Copson's weights are optimal (in fact \emph{critical}). It is shown…

This https://arxiv.org/abs/2312.11661 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Weighted Versions of the Arithmetic-Mean-Geometric Mean Inequality and Zaremba's Function
We use the weighted version of the arithmetic-mean-geometric-mean inequality to motivate new results about Zaremba's function, $z(n) = \sum_{d|n} \frac{\log d}{d}$. We investigate record-setting values for $z(n)$ and the related function $v(n) = \frac{z(n)}{\log τ(n)}$ where $τ(n)$ is the number of divisors of $n$. We show that $v(n)$ takes on a maximum value and we give a list of all record-setting values for$v(n)$. Closely connected inequalities motivate the study of numbers which are …

This https://arxiv.org/abs/2206.08682 has been replaced.
link: https://scholar.google.com/scholar?q=a

Spectral inequality with sensor sets of decaying density for Schrödinger operators with power growth potentials
We prove a spectral inequality (a specific type of uncertainty relation) for Schrödinger operators with confinement potentials, in particular of Shubin-type. The sensor sets are allowed to decay exponentially, where the precise allowed decay rate depends on the potential. The proof uses an interpolation inequality derived by Carleman estimates, quantitative weighted $L^2$-estimates and an $H^1$-concentration estimate, all of them for functions in a spectral subspace of the operator.

Concentration inequalities, dynamical activity, and trade-off relations
Yoshihiko Hasegawa
https://arxiv.org/abs/2402.12197 https://a…

Concentration inequalities, dynamical activity, and trade-off relations
We present a concentration inequality in stochastic thermodynamics that provides a lower bound for the probability distribution of observables in Markov processes, where the lower bound includes the dynamical activity, a central thermodynamic quantity in trade-off relations. The derived inequality is called the thermodynamic concentration inequality. As a first corollary of the thermodynamic concentration inequality, by combining it with the Markov inequality, we derive an upper bound on the ex…

Log-majorization and matrix norm inequalities with application to quantum information
Fumio Hiai
https://arxiv.org/abs/2402.16067 https://

Log-majorization and matrix norm inequalities with application to quantum information
We are concerned with log-majorization for matrices in connection with the multivariate Golden--Thompson trace inequality and the Karcher mean (i.e., a multivariate extension of the weighted geometric mean). We show an extension of Araki's log-majorization and apply it to the $α$-$z$-Rényi divergence in quantum information. We discuss the equality cases in the multivariate trace inequality of Golden--Thompson type and in the norm inequality for the Karcher mean. The paper includes an appendix…

A Minkowski type inequality in warped cylinders
Shujing Pan, Bo Yang
https://arxiv.org/abs/2404.13670 https://arxiv.org/pdf/2404.1367…

A Minkowski type inequality in warped cylinders
We prove a Minkowski type inequality for weakly mean convex and star-shaped hypersurfaces in warped cylinders which are asymptotically flat or hyperbolic. In particular, we show that this sharp inequality holds for outward minimizing hypersurfaces in the Schwarzschild manifold or the hyperbolic space using the weak solution of the inverse mean curvature flow.

On the viscosity linearization method without compactness
Anthony Salib
https://arxiv.org/abs/2403.18860 https://arxiv.org/pdf/2403.1…

On the viscosity linearization method without compactness
Savin's small perturbation approach has had far reaching applications in the theory of non-linear elliptic and parabolic PDE. In this short note, we revisit his seminal proof of De-Giorgi's improvement of flatness theorem for minimal surfaces and provide an approach based on the Harnack inequality that avoids the use of compactness arguments.

On the Spectral Large Sieve Inequality for $\mathrm{PGL}_2 (\mathbb{Z}[i]) \backslash \mathrm{PGL}_2 (\mathbb{C})$
Zhi Qi
https://arxiv.org/abs/2404.09085 …

On the Spectral Large Sieve Inequality for $\mathrm{PGL}_2 (\mathbb{Z}[i]) \backslash \mathrm{PGL}_2 (\mathbb{C})$
In this paper, we introduce concise expressions for the complex Bessel integral that enables us to improve the spectral large sieve inequality of Watt for $\mathrm{PGL}_2 (\mathbb{Z}[i]) \backslash \mathrm{PGL}_2 (\mathbb{C})$. Our result is optimistic in the case when the average of spectral parameters is on a square centered at $(0, 0)$.

Interior pointwise $C^{\alpha}$ regularity for elliptic and parabolic equations with divergence-free drifts
Yuanyuan Lian
https://arxiv.org/abs/2402.18161 …

Interior pointwise $C^α$ regularity for elliptic and parabolic equations with divergence-free drifts
We investigate the interior pointwise $C^α$ regularity for weak solutions of elliptic and parabolic equations with divergence-free drifts. For such equations, the integrability condition on the drift can be relaxed and the interior $C^α$ regularity for some $0<α<1$ has been obtained previously with the aid of Harnack inequality. In this paper, we prove the interior pointwise $C^α$ regularity for any $0<α<1$ provided that the drift is small. We obtain the regularity under three different ty…

The c-d conjecture
Jos\'e I. Latorre, Germ\'an Sierra
https://arxiv.org/abs/2403.17242 https://arxiv.org/pdf/2403.17242

The c-d conjecture
We conjecture a relation between the local dimension $d$ of a local nearest-neighbor critical Hamiltonian in one spatial dimension and the maximum central charge, $c_{\text{max}}$, that it can yield. Specifically, we propose that $c_{\text{max}} \leq d-1$, establishing a link between the short-distance lattice realization of a model and its emerging long-distance entanglement properties. This inequality can be viewed as a general form of a $c$-theorem establishing the reduction of effective deg…

Willmore-type inequalities for closed hypersurfaces in weighted manifolds
Guoqiang Wu, Jia-Yong Wu
https://arxiv.org/abs/2404.16286 https://

Willmore-type inequalities for closed hypersurfaces in weighted manifolds
In this paper, we prove some Willmore-type inequalities for closed hypersurfaces in weighted manifolds with nonnegative Bakry-Émery Ricci curvature. In particular, we give a sharp Willmore-like inequality in shrinking gradient Ricci solitons. These results can be regarded as generalizations of Agostiniani-Fogagnolo-Mazzieri's Willmore-type inequality in weighted manifolds. As applications, we derive some isoperimetric type inequalities under certain existence assumptions of isoperimetric regio…

Interior pointwise $C^{\alpha}$ regularity for elliptic and parabolic equations with divergence-free drifts
Yuanyuan Lian
https://arxiv.org/abs/2402.18161 …

Interior pointwise $C^α$ regularity for elliptic and parabolic equations with divergence-free drifts
We investigate the interior pointwise $C^α$ regularity for weak solutions of elliptic and parabolic equations with divergence-free drifts. For such equations, the integrability condition on the drift can be relaxed and the interior $C^α$ regularity for some $0<α<1$ has been obtained previously with the aid of Harnack inequality. In this paper, we prove the interior pointwise $C^α$ regularity for any $0<α<1$ provided that the drift is small. We obtain the regularity under three different ty…

Extension method in Dirichlet spaces with sub-Gaussian estimates and applications to regularity of jump processes on fractals
Fabrice Baudoin, Quanjun Lang, Yannick Sire
https://arxiv.org/abs/2403.18984

Extension method in Dirichlet spaces with sub-Gaussian estimates and applications to regularity of jump processes on fractals
We investigate regularity properties of some non-local equations defined on Dirichlet spaces equipped with sub-gaussian estimates for the heat kernel associated to the generator. We prove that weak solutions for homogeneous equations involving pure powers of the generator are actually Hölder continuous and satisfy an Harnack inequality. Our methods are based on a version of the Caffarelli-Silvestre extension method which is valid in any Dirichlet space and our results complement the existing l…

This https://arxiv.org/abs/2403.15357 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Duality and Heat flow
We investigate the relation between the Legendre transform of convex functions and heat flow evolution, and how it applies to the functional Blaschke- Santalo inequality, in the wake of the approach proposed by the two last authors.

This https://arxiv.org/abs/2403.15357 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Duality and Heat flow
We investigate the relation between the Legendre transform of convex functions and heat flow evolution, and how it applies to the functional Blaschke- Santalo inequality, in the wake of the approach proposed by the two last authors.

The Spacetime Penrose Inequality for Cohomogeneity One Initial Data
Marcus Khuri, Hari Kunduri
https://arxiv.org/abs/2404.13247 https://

The Spacetime Penrose Inequality for Cohomogeneity One Initial Data
We prove the spacetime Penrose inequality for asymptotically flat $2(n+1)$-dimensional initial data sets for the Einstein equations, which are invariant under a cohomogeneity one action of $\mathrm{SU}(n+1)$. Analogous results are obtained for asymptotically hyperbolic initial data that arise as spatial hypersurfaces in asymptotically Anti de-Sitter spacetimes. More precisely, it is shown that with the dominant energy condition, the total mass is bounded below by an explicit function of the out…

This https://arxiv.org/abs/2402.08527 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A short review on Improvements and stability for some interpolation inequalities
In this paper, we present recent stability results with explicit and dimensionally sharp constants and optimal norms for the Sobolev inequality and for the Gaussian logarithmic Sobolev inequality obtained by the authors in [24]. The stability for the Gaussian logarithmic Sobolev inequality was obtained as a byproduct of the stability for the Sobolev inequality. Here we give a new, direct, alternative proof. We also discuss improved versions of interpolation inequalities based on the carré du c…

This https://arxiv.org/abs/2209.13842 has been replaced.
link: https://scholar.google.com/scholar?q=a

Isoperimetric inequalities for Neumann eigenvalues on bounded domains in rank-1 symmetric spaces
In this paper, we prove sharp isoperimetric inequalities for lower order eigenvalues of Neumann Laplacian on bounded domains in both compact and noncompact rank-1 symmetric spaces. Our results generalize the work of Wang and Xia for bounded domains in the hyperbolic space [13], and Szegö-Weinberger inequality in rank-1 symmetric spaces obtained by Aithal and Santhanam [1].

This https://arxiv.org/abs/2311.13211 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Fractional Caffarelli-Kohn-Nirenberg type inequalities on the Heisenberg group
The aim of this work is to establish some cases of the Caffarelli-Kohn-Nirenberg inequalities on the Heisenberg group for the fractional Sobolev spaces. Here we work with the fractional Sobolev spaces as given by Adimurthi and Mallick in [1]. Our inequalities also give an improvement on the range of indices for the Hardy type inequality established in [1].