Tootfinder

Mixed Christoffel-Minkowski problems for bodies of revolution
Leo Brauner, Georg C. Hofst\"atter, Oscar Ortega-Moreno
https://arxiv.org/abs/2508.09794 https://

Mixed Christoffel-Minkowski problems for bodies of revolution
The mixed Christoffel-Minkowski problem asks for necessary and sufficient conditions for a Borel measure on the Euclidean unit sphere to be the mixed area measure of some convex bodies, one of which, appearing multiple times, is free and the rest are fixed. In the case where all bodies involved are symmetric around a common axis, we provide a complete solution to this problem, without assuming any regularity. In particular, we refine Firey's classification of area measures of figures of revolut…

Spoiler: there is no plan, at least to get to WHO clean air standards.
A failure of leadership, a failure to take on the private car.
Andy Burnham reveals next phase of clean air plan as key deadline looms - Manchester Evening News
https://www.manche…

Andy Burnham reveals next phase of clean air plan as key deadline looms
The CAZ signs recently began to be removed to the tune of hundreds of thousands of pounds

Hausdorff dimension and failure of synthetic curvature bounds in the sub-Lorentzian Heisenberg group
Samu\"el Borza, Chiara Rigoni, Omar Zoghlami
https://arxiv.org/abs/2509.06563

Hausdorff dimension and failure of synthetic curvature bounds in the sub-Lorentzian Heisenberg group
We study the geodesics, Hausdorff dimension, and curvature bounds of the sub-Lorentzian Heisenberg group. Through an elementary variational approach, we provide a new proof of the structure of its maximizing geodesics, showing that they are lifts of hyperbolae coming from a Lorentzian isoperimetric problem in the Minkowski plane. We prove that the Lorentzian Hausdorff dimension of the space is $4$ and that the corresponding measure coincides with the Haar measure. We further establish a novel r…

Capillary rise on hydrogel surfaces
Anagha Datar, Joonas Ryssy, Aku O. Toivonen, Matilda Backholm
https://arxiv.org/abs/2509.08331 https://arxiv.org/pdf/25…

Capillary rise on hydrogel surfaces
Capillary rise occurs when a thin tube contacts a liquid, which rises against gravity due to the capillary force. This phenomenon is present in a wide range of everyday and industrial settings and provides the means to measure the physical properties of liquids. Here, we report on the unusual ultra-slow capillary rise on a solid-like material of agarose hydrogels. The observed meniscus motion cannot be described with classical capillary rise models, and we develop a new model based on the fluid…

Capillary $L_p$ Minkowski Flows
Jinrong Hu, Yingxiang Hu, Mohammad N. Ivaki
https://arxiv.org/abs/2509.06110 https://arxiv.org/pdf/2509.06110

Capillary $L_p$ Minkowski Flows
We study the long-time existence and asymptotic behavior of a class of anisotropic capillary Gauss curvature flows. As an application, we provide a flow approach to the existence of smooth solutions to the capillary even $L_p$ Minkowski problem in the Euclidean half-space for all $p \in (-n-1, \infty)$ and capillary $L_p$ Minkowski problem for $p > n+1$.

Explicit formulae for the Aicardi-Juyumaya bracket of tied links
O'Bryan C\'ardenas-Andaur, Juan Gonz\'alez-Meneses, Marithania Silvero
https://arxiv.org/abs/2510.02075

Explicit formulae for the Aicardi-Juyumaya bracket of tied links
The double bracket $\langle \langle \cdot \rangle \rangle$ (also known as the AJ-bracket) is an invariant of framed tied links that extends the Kauffman bracket of classical links. Unlike the classical setting, little is known about the structure of AJ-states (analogous to classical Kauffman states) of a given tied link diagram, and no general state-sum formula for the AJ-bracket is currently available. In this paper we analyze the AJ-states of $2$- and $3$-tied link diagrams, and provide a com…

Action principle for $\kappa$-Minkowski noncommutative $U(1)$ gauge theory from Lie-Poisson electrodynamics
Maxim Kurkov
https://arxiv.org/abs/2509.03714 https://

Action principle for $κ$-Minkowski noncommutative $U(1)$ gauge theory from Lie-Poisson electrodynamics
Lie-Poisson electrodynamics describes a semi-classical approximation of noncommutative $U(1)$ gauge theories with Lie-algebra-type noncommutativities. We obtain a gauge-invariant local classical action with the correct commutative limit for a generic Lie-Poisson gauge model. At the semi-classical level, our results provide a relatively simple solution to the old problem of constructing an admissible Lagrangian formulation for the $U(1)$ gauge theory on the four-dimensional $κ$-Minkowski space-…

On the Cartan torsion of Minkowskian product of Finsler manifolds
Ranadip Gangopadhyay
https://arxiv.org/abs/2508.03165 https://arxiv.org/pdf/2508.03165

On the Cartan torsion of Minkowskian product of Finsler manifolds
In this paper, we investigate the Cartan torsion and mean Cartan torsion of the Minkowskian product of two Finsler metrics. We derive explicit formulas for both torsions and analyze their geometric behavior. In particular, we demonstrate that both the Cartan torsion and mean Cartan torsion decompose additively if and only if the Minkowskian product is Euclidean. Additionally, we provide a necessary and sufficient condition for the norm of the mean Cartan torsion to remain bounded in the Euclide…

Foundations of Relational Quantum Field Theory I: Scalars
Samuel Fedida, Jan G{\l}owacki
https://arxiv.org/abs/2507.21601 https://arxiv.org/pdf/2507.21601

Foundations of Relational Quantum Field Theory I: Scalars
We develop foundations for a relational approach to quantum field theory (RQFT) based on the operational quantum reference frames (QRFs) framework considered in a relativistic setting. Unlike other efforts in combining QFT with QRFs, we use the latter to provide novel mathematical and conceptual foundations for the former. We focus on scalar fields in Minkowski spacetime and discuss the emergence of relational local (bounded) observables and (pointwise) fields from the consideration of PoincarÃ…

Canonical Reduction Systems in Artin-Tits groups of spherical type
Mar\'ia Cumplido, Juan Gonz\'alez-Meneses, Davide Perego
https://arxiv.org/abs/2510.00713 https://

Canonical Reduction Systems in Artin-Tits groups of spherical type
We introduce the canonical reduction system of an element in an Artin-Tits group of spherical type, which generalizes the similar notion for braids (and mapping classes) introduced by Birman, Lubotzky and McCarthy. We show its basic properties, which coincide with those satisfied in braid groups, and we provide an algorithm to compute it. We improve the algorithm in the case of braid groups, and discuss its complexity in this case. As a necessary result for obtaining the general algorithm, we p…