Results 1 to 10 of about 200 (154)
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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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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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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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 -Hessian equations
Advances in Nonlinear Analysis, 2012 We consider the homogeneous Dirichlet problem for a special -Hessian equation of sub-linear type in a -convex domain , . We study the comparison between the solution of this problem and the (radial) solution of the corresponding problem in a ball having ...
Ahmed Mohammed, Giovanni Porru
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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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On an isoperimetric-isodiametric inequality [PDF]
Analysis & PDE, 2017 Final version to appear in Analysis & PDE.
Andrea Mondino, Emanuele Spadaro
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