Results 11 to 20 of about 520,398 (211)
Notices of the American Mathematical SocietyThe isoperimetric problem is one of the oldest and most famous problems in geometry.
Eichmair, Michael, Brendle, Simon
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Isoperimetric Inequalities Made Simpler
Discrete AnalysisIsoperimetric 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 +3 more
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On an isoperimetric-isodiametric inequality [PDF]
Analysis & PDE, 2017 The Euclidean mixed isoperimetric-isodiametric inequality states that the round ball maximizes the volume under constraint on the product between boundary area and radius. The goal of the paper is to investigate such mixed isoperimetric-isodiametric inequalities in Riemannian manifolds.
Andrea Mondino, Emanuele Spadaro
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Entropic Isoperimetric Inequalities
, 2023 We discuss optimal bounds on the Rényi entropies in terms of the Fisher information. In Information Theory, such relations are also known as entropic isoperimetric inequalities.
Bobkov, Sergey, Roberto, Cyril
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An Asymptotic Isoperimetric Inequality [PDF]
Geometric And Functional Analysis, 1998 For a finite metric space \(V\) with a metric \(\rho\) and probability measure \(\mu\), let \(V^n\) be the product metric space in which the distance between \(a= (a_1,\dots, a_n)\) and \(b= (b_1,\dots, b_n)\) is \(\rho_n(a,b)= \sum_i\rho(a_i, b_i)\) and the measure \(\mu_n(a_1,\dots, a_n)= \prod_i\mu(a_i)\). For any \(d\geq 0\) the \(d\)-neighbourhood
Alon, N., Boppana, R., Spencer, J.
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Sobolev inequality and isoperimetric inequality for submanifolds in a smooth metric measure space
, 2023 Brendle recently proved a sharp Sobolev inequality and logarithmic Sobolev inequality for submanifolds in Euclidean space. From the sharp Sobolev inequality, he achieved a breakthrough in the conjecture of isoperimetric inequality for minimal ...
Ho, Pak-tung
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Generalized isoperimetric inequalities [PDF]
Journal of Mathematical Physics, 1973 New inequalities for certain Green's functions are given. They may be interpreted physically in many ways, for example, as applying to the quantum mechanical motion of a particle in a potential or to diffusion in the presence of absorbers. These inequalities involve a symmetrization process very closely related to Steiner symmetrization used in the ...
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Randomized Isoperimetric Inequalities [PDF]
, 2017 We discuss isoperimetric inequalities for convex sets. These include the classical isoperimetric inequality and that of Brunn-Minkowski, Blaschke-Santalo, Busemann-Petty and their various extensions. We show that many such inequalities admit stronger randomized forms in the following sense: for natural families of associated random convex sets one has ...
Paouris, Grigoris, Pivovarov, Peter
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Thermodynamic instabilities of generalized exotic BTZ black holes
Journal of High Energy Physics, 2019 We examine the conjecture that black holes violating the reverse isoperimetric inequality have negative specific heat at constant volume C V [1]. We test this conjecture on the family of generalized exotic Bañados, Teitelboim and Zanelli (BTZ) black ...
Wan Cong, Robert B. Mann
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On singular quasilinear elliptic equations with data measures
Advances in Nonlinear Analysis, 2021 The aim of this work is to study a quasilinear elliptic equation with singular nonlinearity and data measure. Existence and non-existence results are obtained under necessary or sufficient conditions on the data, where the main ingredient is the ...
Alaa Nour Eddine +2 more
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