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Isoperimetric Inequalities Made Simpler [PDF]
arXiv.org, 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 ...
Ronen Eldan +3 more
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Generalized isoperimetric inequalities. [PDF]
Proc Natl Acad Sci U S A, 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 ...
Luttinger JM.
europepmc +4 more sources
Bonnesen-style Wulff isoperimetric inequality [PDF]
Journal of Inequalities and Applications, 2017 The Wulff isoperimetric inequality is a natural extension of the classical isoperimetric inequality (Green and Osher in Asian J. Math. 3:659-676 1999). In this paper, we establish some Bonnesen-style Wulff isoperimetric inequalities and reverse Bonnesen ...
Zengle Zhang, Jiazu Zhou
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Weighted quantitative isoperimetric inequalities in the Grushin space R h + 1 ${R}^{h+1}$ with density | x | p $|x|^{p}$ [PDF]
Journal of Inequalities and Applications, 2017 In this paper, we prove weighted quantitative isoperimetric inequalities for the set E α = { ( x , y ) ∈ R h + 1 : | y | < ∫ arcsin | x | π 2 sin α + 1 ( t ) d t , | x | < 1 } $E_{\alpha}= \{(x,y)\in {R}^{h+1}: \vert y \vert
Guoqing He, Peibiao Zhao
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Bonnesen-style inequality for the first eigenvalue on a complete surface of constant curvature [PDF]
Journal of Inequalities and Applications, 2017 By Cheeger’s isoperimetric constants, some lower bounds and upper bounds of λ 1 $\lambda_{1}$ , the first eigenvalue on a complete surface of constant curvature, are given.
Niufa Fang, Jiazu Zhou
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From Rényi Entropy Power to Information Scan of Quantum States [PDF]
Entropy, 2021 In this paper, we generalize the notion of Shannon’s entropy power to the Rényi-entropy setting. With this, we propose generalizations of the de Bruijn identity, isoperimetric inequality, or Stam inequality. This framework not only allows for finding new
Petr Jizba +2 more
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Computational Hardness of Collective Coin-Tossing Protocols [PDF]
Entropy, 2020 Ben-Or and Linial, in a seminal work, introduced the full information model to study collective coin-tossing protocols. Collective coin-tossing is an elegant functionality providing uncluttered access to the primary bottlenecks to achieve security in a ...
Hemanta K. Maji
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Randomized Isoperimetric Inequalities [PDF]
, 2016 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.
G. Paouris, P. Pivovarov
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Sobolev type inequalities for compact metric graphs [PDF]
Journal of Inequalities and Applications, 2018 In this paper analogues of Sobolev inequalities for compact and connected metric graphs are derived. As a consequence of these inequalities, a lower bound, commonly known as Cheeger inequality, on the first non-zero eigenvalue of the Laplace operator ...
Muhammad Usman
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Isoperimetric Inequalities for the Magnetic Neumann and Steklov Problems with Aharonov–Bohm Magnetic Potential [PDF]
Journal of Geometric Analysis, 2022 We discuss isoperimetric inequalities for the magnetic Laplacian on bounded domains of R2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs ...
B. Colbois, Luigi Provenzano, A. Savo
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