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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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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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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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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.
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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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Isoperimetric Inequalities for Convex Cones [PDF]
Proceedings of the American Mathematical Society, 1990 We present here an isoperimetric inequality for sets contained in a convex cone. Some applications to symmetrization problems and Sobolev inequalities are also indicated.
LIONS P. L., PACELLA, Filomena
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Isoperimetric inequalities in graphs and surfaces [PDF]
Electronic Notes in Discrete Mathematics, 2014 Let M be the set of metric spaces that are either graphs with bounded degree or Riemannian manifolds with bounded geometry. Kanai proved the quasi-isometric stability of several geometric properties (in particular, of isoperimetric inequalities) for the spaces in M.
Cantón Pire, Alicia +3 more
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