Results 61 to 70 of about 654,419 (234)

Index of minimal spheres and isoperimetric eigenvalue inequalities [PDF]

Inventiones Mathematicae, 2019
In the present paper we use twistor theory in order to solve two problems related to harmonic maps from surfaces to Euclidean spheres Sn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb ...
Mikhail Karpukhin
semanticscholar   +1 more source

Isoperimetric inequalities on slabs with applications to cubes and Gaussian slabs

Communications on Pure and Applied Mathematics, Volume 79, Issue 4, Page 1012-1072, April 2026.
Abstract We study isoperimetric inequalities on “slabs”, namely weighted Riemannian manifolds obtained as the product of the uniform measure on a finite length interval with a codimension‐one base. As our two main applications, we consider the case when the base is the flat torus R2/2Z2$\mathbb {R}^2 / 2 \mathbb {Z}^2$ and the standard Gaussian measure
Emanuel Milman
wiley   +1 more source

Isoperimetric inequalities in unbounded convex bodies [PDF]

Memoirs of the American Mathematical Society, 2016
We consider the problem of minimizing the relative perimeter under a volume constraint in an unbounded convex body C ⊂ R n C\subset \mathbb {R}^{n} , without assuming any further regularity on the boundary of C C ...
G. P. Leonardi, Manuel Ritor'e, Efstratios Vernadakis   +2 more
semanticscholar   +1 more source

Sublinear bilipschitz equivalence and the quasiisometric classification of solvable Lie groups

Journal of the London Mathematical Society, Volume 113, Issue 4, April 2026.
Abstract We prove a product theorem for sublinear bilipschitz equivalences which generalizes the classical work of Kapovich, Kleiner, and Leeb on quasiisometries between product spaces. We employ our product theorem to distinguish up to quasiisometry certain families of solvable groups which share the same dimension, cone‐dimension and Dehn function ...
Ido Grayevsky, Gabriel Pallier
wiley   +1 more source

Quantitative isoperimetric inequalities for log-convex probability measures on the line

, 2014
The purpose of this paper is to analyze the isoperimetric inequality for symmetric log-convex probability measures on the line. Using geometric arguments we first re-prove that extremal sets in the isoperimetric inequality are intervals or complement of ...
Feo, F., Posteraro, M. R., Roberto, C.
core   +3 more sources

Sharp Isoperimetric Inequalities for Small Volumes in Complete Noncompact Riemannian Manifolds of Bounded Geometry Involving the Scalar Curvature [PDF]

International mathematics research notices, 2016
We provide an isoperimetric comparison theorem for small volumes in an $n$-dimensional Riemannian manifold $(M^n,g)$ with $C^3$ bounded geometry in a suitable sense involving the scalar curvature function.
S. Nardulli, Luis Eduardo Osorio Acevedo
semanticscholar   +1 more source

Semiclassical inequalities for Dirichlet and Neumann Laplacians on convex domains

Communications on Pure and Applied Mathematics, Volume 79, Issue 3, Page 762-822, March 2026.
Abstract We are interested in inequalities that bound the Riesz means of the eigenvalues of the Dirichlet and Neumann Laplacians in terms of their semiclassical counterpart. We show that the classical inequalities of Berezin–Li–Yau and Kröger, valid for Riesz exponents γ≥1$\gamma \ge 1$, extend to certain values γ<1$\gamma <1$, provided the underlying ...
Rupert L. Frank, Simon Larson
wiley   +1 more source

Isoperimetric Inequalities Made Simpler

Discrete Analysis
Isoperimetric inequalities made simpler, Discrete Analysis 2025:7, 23 pp. The famous isoperimetric inequality in the plane states that of all (sufficiently nice) shapes with a given volume, the one with the smallest boundary length is a circle.
Ronen Eldan, Guy Kindler, Noam Lifshitz, Dor Minzer   +3 more
doaj   +1 more source

Reversed Stein–Weiss Inequalities with Poisson-Type Kernel and Qualitative Analysis of Extremal Functions

Advanced Nonlinear Studies, 2021
Through conformal map, isoperimetric inequalities are equivalent to the Hardy–Littlewood–Sobolev (HLS) inequalities involved with the Poisson-type kernel on the upper half space.
Tao Chunxia
doaj   +1 more source

Isoperimetric inequalities for finite perimeter sets under lower Ricci curvature bounds [PDF]

Rendiconti Lincei - Matematica e Applicazioni, 2016
We prove that the results regarding the Isoperimetric inequality and Cheeger constant formulated in terms of the Minkowski content, obtained by the authors in previous papers in the framework of essentially non-branching metric measure spaces verifying ...
Fabio Cavalletti, Andrea Mondino
semanticscholar   +1 more source