Results 51 to 60 of about 654,419 (234)

The Isoperimetric Inequality

Notices of the American Mathematical Society
Comment: to appear in Notices Amer.
Eichmair, Michael, Brendle, Simon
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Exact Face-isoperimetric Inequalities

European Journal of Combinatorics, 1990
Let \([p]^ N\) be the grid, i.e. \([p]^ N=\{0,1,...,N-1\}\). The authors give the best possible upper bound for the number of faces of a fixed dimension contained in a subset of the grid. As a conjecture the result appeared in \textit{B. Bollobás} and \textit{A. J. Radcliffe} [Eur. J. Comb. 11, No.4, 323-333 (1990; see the review above)].
Bollobás, Béla, Leader, Imre
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Analytic isoperimetric inequalities [PDF]

Mathematical Inequalities & Applications, 2000
It is known that the classical geometric isoperimetric inequalities are equivalent to suitable analytic isoperimetric inequalities. For example, the analytic isoperimetric inequality \[ \left( \sum_{i=1}^{n}\sin \theta _{i}\right) ^{2}\geq d_{n}(\sigma)\sum_{i=1}^{n}\sin \theta _{i}\cos \theta _{i}+ \left(n\sin \sigma -\sum_{i=1}^{n}\sin \theta _{i ...
Ku, Hsu-Tung, Ku, Mei-Chin
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Poincaré, modified logarithmic Sobolev and isoperimetric inequalities for Markov chains with non-negative Ricci curvature [PDF]

Journal of Functional Analysis, 2016
We study functional inequalities for Markov chains on discrete spaces with entropic Ricci curvature bounded from below. Our main results are that when curvature is non-negative, but not necessarily positive, the spectral gap, the Cheeger isoperimetric ...
Matthias Erbar, M. Fathi
semanticscholar   +1 more source

Lp Affine Isoperimetric Inequalities [PDF]

Journal of Differential Geometry, 2000
An affine isoperimetric inequality compares two functionals associated with convex (or more general) bodies, where the ratio of the functionals is invariant under non-degenerate linear transformations. The article deals with affine isoperimetric inequalities for centroid and projection bodies. The most important inequality concerning centroid bodies is
Lutwak, Erwin, Yang, Deane, Zhang, Gaoyong   +2 more
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Isoperimetric inequalities in nonlocal diffusion problems with integrable kernel [PDF]

Opuscula Mathematica
We 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
doaj   +1 more source

Interpolated inequalities between exponential and Gaussian, Orlicz hypercontractivity and isoperimetry

, 2004
We introduce and study a notion of Orlicz hypercontractive semigroups. We analyze their relations with general $F$-Sobolev inequalities, thus extending Gross hypercontractivity theory.
Barthe, F., Cattiaux, P., Roberto, C.
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On Non Local p-Laplacian with Right Hand Side Radon Measure

Fractal and Fractional, 2022
The aim of this paper is to investigate the following non local p-Laplacian problem with data a bounded Radon measure ϑ∈Mb(Ω): (−Δ)psu=ϑinΩ, with vanishing conditions outside Ω, and where s∈(0,1),2 ...
Mohammed Kbiri Alaoui
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Inequalities for general mixed affine surface areas

, 2011
Several general mixed affine surface areas are introduced. We prove some important properties, such as, affine invariance, for these general mixed affine surface areas.
Ye, Deping
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Almost euclidean Isoperimetric Inequalities in spaces satisfying local Ricci curvature lower bounds. [PDF]

, 2017
Motivated by Perelman's Pseudo Locality Theorem for the Ricci flow, we prove that if a Riemannian manifold has Ricci curvature bounded below in a metric ball which moreover has almost maximal volume, then in a smaller ball (in a quantified sense) it ...
Fabio Cavalletti, Andrea Mondino
semanticscholar   +1 more source