Isotropic measures and stronger forms of the reverse isoperimetric inequality

A stability version of the reverse isoperimetric inequality, and the corresponding inequality for isotropic measures are established.

[1]  K. Böröczky,et al.  Affine images of isotropic measures , 2015 .

[2]  M. Henk,et al.  Cone-volume measure and stability , 2014, 1407.7272.

[3]  Silouanos Brazitikos Geometry of Isotropic Convex Bodies , 2014 .

[4]  F. Barthe,et al.  Invariances in variance estimates , 2011, 1106.5985.

[5]  Bo'az Klartag,et al.  Centroid Bodies and the Logarithmic Laplace Transform - A Unified Approach , 2011, 1103.2985.

[6]  L. Duembgen Bounding Standard Gaussian Tail Probabilities , 2010, 1012.2063.

[7]  O. Guédon,et al.  Interpolating Thin-Shell and Sharp Large-Deviation Estimates for Lsotropic Log-Concave Measures , 2010, 1011.0943.

[8]  A. Figalli,et al.  A mass transportation approach to quantitative isoperimetric inequalities , 2010 .

[9]  A. Figalli,et al.  A refined Brunn-Minkowski inequality for convex sets , 2009 .

[10]  M. Ledoux,et al.  Correlation and Brascamp–Lieb Inequalities for Markov Semigroups , 2009, 0907.2858.

[11]  N. Fusco,et al.  The sharp quantitative isoperimetric inequality , 2008 .

[12]  B. Klartag On nearly radial marginals of high-dimensional probability measures , 2008, 0810.4700.

[13]  E. Carlen,et al.  Subadditivity of The Entropy and its Relation to Brascamp–Lieb Type Inequalities , 2007, 0710.0870.

[14]  B. Klartag,et al.  A Berry-Esseen type inequality for convex bodies with an unconditional basis , 2007, 0705.0832.

[15]  E. Lutwak,et al.  Volume inequalities for isotropic measures , 2006, math/0607753.

[16]  Franz E Schuster,et al.  An arithmetic proof of John’s ellipsoid theorem , 2005, 1207.7246.

[17]  T. Tao,et al.  The Brascamp–Lieb Inequalities: Finiteness, Structure and Extremals , 2005, math/0505065.

[18]  E. Lutwak,et al.  Volume Inequalities for Subspaces of L p , 2004 .

[19]  K. Ball Chapter 4 – Convex Geometry and Functional Analysis , 2001 .

[20]  Apostolos Giannopoulos,et al.  Isotropic surface area measures , 1999 .

[21]  F. Barthe On a reverse form of the Brascamp-Lieb inequality , 1997, math/9705210.

[22]  Franck Barthe,et al.  Inégalités de Brascamp-Lieb et convexité , 1997 .

[23]  Miklós Simonovits,et al.  Isoperimetric problems for convex bodies and a localization lemma , 1995, Discret. Comput. Geom..

[24]  K. Ball CONVEX BODIES: THE BRUNN–MINKOWSKI THEORY , 1994 .

[25]  R. Schneider Convex Bodies: The Brunn–Minkowski Theory: Minkowski addition , 1993 .

[26]  E. Lieb Gaussian kernels have only Gaussian maximizers , 1990 .

[27]  H. Groemer Stability properties of geometric inequalities , 1990 .

[28]  Keith Ball,et al.  Volume Ratios and a Reverse Isoperimetric Inequality , 1989, math/9201205.

[29]  H. Groemer,et al.  On the Brunn-Minkowski theorem , 1988 .

[30]  E. Lieb,et al.  Best Constants in Young's Inequality, Its Converse, and Its Generalization to More than Three Functions , 1976 .

[31]  C. Petty Surface area of a convex body under affine transformations , 1961 .

[32]  B. Grünbaum Partitions of mass-distributions and of convex bodies by hyperplanes. , 1960 .

[33]  W. Gustin An isoperimetric minimax , 1953 .

[34]  R. D. Gordon Values of Mills' Ratio of Area to Bounding Ordinate and of the Normal Probability Integral for Large Values of the Argument , 1941 .

[35]  F. Behrend Über einige Affininvarianten konvexer Bereiche , 1937 .

[36]  F. John Polar correspondence with respect to a convex region , 1937 .

[37]  P. Gruber,et al.  Convex and Discrete Geometry , 2007 .

[38]  F. Barthe A Continuous Version of the Brascamp-Lieb Inequalities , 2004 .

[39]  V. Milman,et al.  Chapter 17 - Euclidean Structure in Finite Dimensional Normed Spaces , 2001 .

[40]  H. Groemer,et al.  Stability of Geometric Inequalities , 1993 .

[41]  E. Lutwak Selected Affine Isoperimetric Inequalities , 1993 .

[42]  R. Schneider,et al.  Stability Estimates for some Geometric Inequalities , 1991 .

[43]  K. Ball Volumes of sections of cubes and related problems , 1989 .

[44]  V. I. Diskant Stability of the solution of the Minkowski equation , 1973 .

[45]  A. A. Giannopoulos,et al.  Institute for Mathematical Physics Extremal Problems and Isotropic Positions of Convex Bodies Extremal Problems and Isotropic Positions of Convex Bodies , 2022 .