Results 11 to 20 of about 13,857 (195)
A sharp reverse Bonnesen-style inequality and generalization
Journal of Inequalities and Applications, 2019 We investigate the isoperimetric deficit of the oval domain in the Euclidean plane. Via the kinematic formulae of Poincaré and Blaschke, and Blaschke’s rolling theorem, we obtain a sharp reverse Bonnesen-style inequality for a plane oval domain, which ...
Pengfu Wang
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Dilation Type Inequalities for Strongly-Convex Sets in Weighted Riemannian Manifolds
Analysis and Geometry in Metric Spaces, 2021 In this paper, we consider a dilation type inequality on a weighted Riemannian manifold, which is classically known as Borell’s lemma in high-dimensional convex geometry.
Tsuji Hiroshi
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Courant-sharp eigenvalues of the three-dimensional square torus [PDF]
, 2015 In this paper, we determine, in the case of the Laplacian on the flat three-dimensional torus $(\mathbb{R}/\mathbb{Z})^3$, all the eigenvalues having an eigenfunction which satisfies the Courant nodal domains theorem with equality (Courant-sharp ...
Léna, Corentin
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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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Reifenberg’s isoperimetric inequality revisited [PDF]
Calculus of Variations and Partial Differential Equations, 2019 We prove a generalization of Reifenberg's isoperimetric inequality. The main result of this paper is used to establish existence of a minimizer for an anisotropically-weighted area functional among a collection of surfaces which satisfies a set of axioms, namely being closed under certain deformations and Hausdorff limits.
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Isoperimetric Inequalities Made Simpler
, 2022 We give an alternative, simple method to prove isoperimetric inequalities over the hypercube. In particular, we show: 1. An elementary proof of classical isoperimetric inequalities of Talagrand, as well as a stronger isoperimetric result conjectured by Talagrand and recently proved by Eldan and Gross. 2. A strengthening of the Friedgut junta theorem,
Eldan, Ronen +3 more
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Relative Isoperimetric Inequality for Minimal Submanifolds in a Riemannian Manifold
Journal of Inequalities and Applications, 2010 Let Σ be a domain on an m-dimensional minimal submanifold in the outside of a convex set C in 𝕊n or ℍn. The modified volume M(Σ) is introduced by Choe and Gulliver (1992) and we prove a sharp modified relative isoperimetric
Juncheol Pyo
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Isoperimetric inequalities in nonlocal diffusion problems with integrable kernel [PDF]
Opuscula MathematicaWe deduce isoperimetric estimates for solutions of linear stationary and evolution problems. Our main result establishes the comparison in norm between the solution of a problem and its symmetric version when nonlocal diffusion defined through integrable
Gonzalo Galiano
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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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Geometric inequalities from phase space translations [PDF]
, 2016 We establish a quantum version of the classical isoperimetric inequality relating the Fisher information and the entropy power of a quantum state. The key tool is a Fisher information inequality for a state which results from a certain convolution ...
Anna Vershynina +9 more
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