Tootfinder

Isoperimetric profiles of lamplighter-like groups
Corentin Correia, Vincent Dumoncel
https://arxiv.org/abs/2506.13235 https://arxiv.o…

Isoperimetric profiles of lamplighter-like groups
Given a finitely generated amenable group $H$ satisfying some mild assumptions, we relate isoperimetric profiles of the lampshuffler group $\mathsf{Shuffler}(H)=\mathsf{FSym}(H)\rtimes H$ to those of $H$. Our results are sharp for all exponential growth groups for which isoperimetric profiles are known, including Brieussel-Zheng groups. This refines previous estimates obtained by Erschler and Zheng and by Saloff-Coste and Zheng. The most difficult part is to find an optimal upper bound, and our…

O Lovecraft havia de fazer disto uma história cheia de tentšculos.
https://masto.pt/@sapopt/114699066673500829

Isoperimetric Problem and Weierstrass Necessary Condition for Fractional Calculus of Variations
Shakir Sh. Yusubov, Shikhi Sh. Yusubov, Elimhan N. Mahmudov
https://arxiv.org/abs/2506.12926

Isoperimetric Problem and Weierstrass Necessary Condition for Fractional Calculus of Variations
Summary]{In this paper, we study problems of minimization of a functional depending on the fractional Caputo derivative of order $0<α\leq 1$ and the fractional Riemann- Liouville integral of order $β> 0$ at fixed endpoints. A fractional analogue of the Du Bois-Reymond lemma is proved, and the Euler-Lagrange conditions are proved for the simplest problem of fractional variational calculus with fixed ends and for the fractional isoperimetric problem. An approach is proposed to obtain the necess…

A Geometric Solution to the Isoperimetric Problem and its Quantitative Inequalities
Lakshya Chaudhary
https://arxiv.org/abs/2506.12864 https://

A Geometric Solution to the Isoperimetric Problem and its Quantitative Inequalities
This paper introduces a geometric solution to the classical isoperimetric problem by analysing the area efficiency of n-sided regular polygons through a novel apothem-hypotenuse ratio framework. A new formula is derived to quantify polygonal efficiency based on apothem, hypotenuse, and perimeter, demonstrating how regular polygons approach the optimal area-enclosing efficiency of the circle as the number of sides increases. The work further presents an original formula for area lost relative to…

Isoperimetric Inequality on Manifolds with Quadratically Decaying Curvature
Dangyang He
https://arxiv.org/abs/2506.13365 https://arxi…

Isoperimetric Inequality on Manifolds with Quadratically Decaying Curvature
In this paper, we investigate the reverse improvement property of Sobolev inequalities on manifolds with quadratically decaying Ricci curvature. Specifically, we establish conditions under which the uniform decay of the heat kernel implies the validity of an isoperimetric inequality. As an application, we demonstrate the existence of isoperimetric sets in generalized Grushin spaces. Our approach is built on a weak-type Sobolev inequality, gradient estimates on remote balls, and a Hardy-type glu…

A survey of UK academic integrity violations finds nearly 7,000 proven AI cheating cases in 2023-24, or 5.1 per 1,000 students, up from 1.6 per 1,000 in 2022-23 (Michael Goodier/The Guardian)
https://www.theguardian.co…

What’s brewing?
#StudioVibes
#WorkInProgress

Protest filling the street at 24th and Mission in San Francisco
#ICEProtests #FuckICE

E-scooter injury toll revealed in study just ‘tip of the iceberg’ in Australia, doctors warn | Road safety | The Guardian
https://www.theguardian.com/world/2025/jun/04/e-scooter-injury-toll-reve…

Sending “300 now, 2000 eventually” into a dynamic environment where there could easily be 10X as many hostiles is a recipe for disaster. Maybe an intentional one to generate a Reichstag Fire event.
#LosAngeles #ICEProtests