Affine isoperimetric inequality

Author: awfi

August undefined, 2024

WebMar 6, 2014 · New Orlicz Affine Isoperimetric Inequalities Authors: Deping Ye Memorial University of Newfoundland Abstract The Orlicz-Brunn-Minkowski theory receives considerable attention recently, and many... WebWe introduce floating bodies for convex, not necessarily bounded subsets of Rn. This allows us to define floating functions for convex and log concave functions and log concave measures. We establish the asymptotic behavior of the integral difference of a log concave function and its floating function. This gives rise to a new affine invariant which bears …

THE LOGARITHMIC MINKOWSKI PROBLEM - JSTOR

WebJan 1, 1993 · The affine isoperimetric inequality The affine isoperimetric inequality states that for K e §P, ()+] ^ 2+ V (K)n-x, (AI) with equality if and only if K is an ellipsoid. For a somewhat more restricted class of bodies, and n ^ 3, this inequality is due to Blaschke (1916) (see also Blaschke 1923). WebSep 10, 2024 · Unlike the classical isoperimetric inequalities, the affine isoperimetric inequalities are inequalities between a pair of geometric functionals whose product is … kids at play therapy ipswich

王卫东个人简介-三峡大学理学院

WebSeptember, 2000 L p Affine Isoperimetric Inequalities Erwin Lutwak , Deane Yang , Gaoyong Zhang J. Differential Geom. 56(1): 111-132 (September, 2000). WebWe give a stability version of of the Blaschke-Santaló inequality in the plane. Skip to search form Skip to main content Skip to account menu. Semantic Scholar's Logo. Search 211,553,455 papers from all fields of science. Search. Sign In … WebJun 20, 2008 · Introduction An affine isoperimetric inequality relates two functionals associated with convex bodies (or more general sets) where the ratio of the functionals is … kids at school clip art black and white

Functional affine-isoperimetry and an inverse logarithmic Sobolev ...

WebAug 6, 2024 · We also study its first eigenvalue λ1,pA(Ω)which satisfies the corresponding affine Faber-Krahn inequality, that is, λ1,pA(Ω)is minimized (among sets of equal volume) only when Ω is an ellipsoid. This point depends fundamentally on the PDEs regularity analysis aimed at the operator ΔpAf. WebUsing Colesanti and Fragalà’s first variation formula, we define the geominimal surface area for log-concave functions, and its related affine isoperimetric inequality is also established. 1. Introduction As we have known, Minkowski addition (the vector addition of convex bodies) is the cornerstone in the classical Brunn-Minkowski theory. kids at school pictureWebAn aﬃne isoperimetric inequality compares two functionals associ-ated with convex (or more general) bodies, where the ratio of the func-tionals is invariant under non … kids at school coloring page

"WebOct 20, 2024 · Sharp Isoperimetric Inequalities For Affine Quermassintegrals Abstract The affine quermassintegrals associated to a convex body in $\R^n$ are affine-invariant … " - Affine isoperimetric inequality

Affine isoperimetric inequality

Affine Isoperimetric Inequalities Request PDF - ResearchGate

WebApr 30, 2024 · Affine vs. Euclidean isoperimetric inequalities Christoph Haberl, Franz E. Schuster It is shown that every even, zonal measure on … WebNov 7, 2024 · Over the last two decades several important affine isoperimetric inequalities, comparing geometric functionals which are invariant under volume …

Did you know?

Webinequalities. It is also either known or conjectured that these same in-variants, when restricted to convex bodies, satisfy sharp reverse a ne isoperimetric inequalities, where the extremal bodies are simplices, in contrast to the sharp a ne isoperimetric inequalities, where the ex-tremal bodies are ellipsoids. See, for example, [19,21,26{28,38 ... WebA purely analytic proof is given for an inequality that has as a direct consequence the two most important affine isoperimetric inequalities of plane convex geometry: The …

WebNov 10, 2010 · A stability version of the Blaschke–Santaló inequality and the affine isoperimetric inequality for convex bodies of dimension n ⩾ 3 is proved. The first step is the reduction to the case when the convex body is o -symmetric and has axial rotational symmetry. This step works for related inequalities compatible with Steiner symmetrization. WebEmanuel Milman Sharp isoperimetric inequality for afﬁne quermassintegrals. Rank one cases k 2f1;n 1g Rank onecases k 2f1;n 1gof Lutwak’s conjecture areclassical: ... Sharp …

WebAbstract. We give a functional version of the affine isoperimetric inequality for log-concave functions which may be interpreted as an inverse form of a logarithmic Sobolev inequality for entropy. A linearization of this inequality gives an inverse inequality to the Poincaré inequality for the Gaussian measure. Original language. WebMay 10, 2024 · In addition, we address a related conjecture of Lutwak on the validity of certain Alexandrov-Fenchel-type inequalities for affine (and more generally $L^p$-moment) quermassintegrals. The case...

WebA sharp reverse affine isoperimetric inequality for Borel measures on the sphere is presented. This leads to sharp reverse affine isoperimetric inequalities for convex bodies. AB - Necessary and sufficient conditions are given in order for a Borel measure on the Euclidean sphere to have an affine image that is isotropic.

WebJun 5, 2012 · Applications of the Lp-surface area measure to affine isoperimetric inequalities were given in, e.g., [6], [40], and [45]. THE LOGARITHMIC MINKOWSKI PROBLEM 833 The following Lp-Minkowski problem is one of the central problems in contem-porary convex geometric analysis. Lp-Minkowski problem. Find necessary and … is mexico high contextWebMar 26, 2024 · One of the most important affine isoperimetric inequalities (cf. Isoperimetric inequality). It has applications to number theory, differential equations, differential geometry, stochastic geometry, as well as in the study of Banach spaces. kids at school picturesWebJan 5, 2001 · Affine Isoperimetric Inequalities Authors: Erwin Lutwak Polytechnic Institute of New York University Deane Yang New York University Gaoyong Zhang Abstract this article deals with inequalities... kids attachment to objectsWebAug 1, 2011 · In this paper, we establish a number of L p-affine isoperimetric inequalities for L p-geominimal surface area. In particular, we obtain a Blaschke–Santaló type inequality and a cyclic inequality between different L p-geominimal surface areas of a convex body. Keywords. 52A40. Type kids at school pngWebMay 10, 2024 · Sharp Isoperimetric Inequalities for Affine Quermassintegrals Emanuel Milman, Amir Yehudayoff The affine quermassintegrals associated to a convex body in are affine-invariant analogues of the classical intrinsic volumes from the Brunn-Minkowski theory, and thus constitute a central pillar of affine convex geometry. kidsatthecreek.comWebSep 10, 2024 · One of the basic affine isoperimetric inequalities is Petty’s projection inequality : among convex bodies of given volume, the ones whose polar projection bodies have maximal volume are precisely the ellipsoids. kids at show and tell cartoonWebIn mathematics, the Brunn–Minkowski theorem (or Brunn–Minkowski inequality) is an inequality relating the volumes (or more generally Lebesgue measures) of compact subsets of Euclidean space.The original version of the Brunn–Minkowski theorem (Hermann Brunn 1887; Hermann Minkowski 1896) applied to convex sets; the generalization to compact … kids at the creek bothell