Convex Geometric Analysis

by Edited by Keith M. Ball , Vitali Milman

• ISBN13: 9780521642590
• ISBN10: 0521642590
• Format: Hardcover
• Copyright: 1999-01-28
• Publisher: Cambridge University Press

Summary

Convex geometry is at once simple and amazingly rich. While the classical results go back many decades, during the last ten years the integral geometry of convex bodies has undergone a dramatic revitalization, brought about by the introduction of methods, results and, most importantly, new viewpoints, from probability theory, harmonic analysis and the geometry of finite-dimensional normed spaces. This book is a collection of research and expository articles on convex geometry and probability, suitable for researchers and graduate students in several branches of mathematics coming under the broad heading of 'Geometric Functional Analysis'. It continues the Israel GAFA Seminar series, which is widely recognized as the most useful research source in the area. The collection reflects the work done at the program in Convex Geometry and Geometric Analysis that took place at MSRI in 1996, emphasizing the links between the geometry of convex bodies, probability theory, harmonic analysis and recent probabilistic methods in computation.

Table of Contents

Introduction: The Convex Geometry and Geometric Analysis Program, MSRI, Spring 1996	ix	(2)
Program Seminars	xi	(8)
GAFA Seminars 1994-1996	xix
Integrals of Smooth and Analytic Functions over Minkowski's Sums of Convex Sets	1	(16)
SEMYON ALESKER
Localization Technique on the Sphere and the Gromov-Milman Theorem on the Concentration Phenomenon on Uniformly Convex Sphere	17	(12)
SEMYON ALESKER
Geometric Inequalities in Option Pricing	29	(24)
CHRISTER BORELL
Random Points in Isotropic Convex Sets	53	(6)
JEAN BOURGAIN
Threshold Intervals under Group Symmetries	59	(6)
JEAN BOURGAIN
GIL KALAI
On a Generalization of the Busemann-Petty Problem	65	(12)
JEAN BOURGAIN
GAOYONG ZHANG
Isotropic Constants of Schatten Class Spaces	77	(4)
SEAN DAR
On the Stability of the Volume Radius	81	(8)
EFIM D. GLUSKIN
Polytope Approximations of the Unit Ball of l^n(p)	89	(22)
W. TIMOTHY GOWERS
A Remark about the Scalar-Plus-Compact Problem	111	(6)
W. TIMOTHY GOWERS
Another Low-Technology Estimate in Convex Geometry	117	(6)
GREG KUPERBERG
On the Equivalence Between Geometric and Arithmetic Means for Log-Concave Measures	123	(6)
RAFAL LATALA
On the Constant in the Reverse Brunn-Minkowski Inequality for p-Convex Balls	129	(10)
ALEXANDER E. LITVAK
The Extension of the Finite-Dimensional Version of Krivine's Theorem to Quasi-Normed Spaces	139	(10)
ALEXANDER E. LITVAK
A Note on Gowers' Dichotomy Theorem	149	(10)
BERNARD MAUREY
An "Isomorphic" Version of Dvoretzky's Theorem, II	159	(6)
VITALI MILMAN
GIDEON SCHECHTMAN
Asymptotic Versions of Operators and Operator Ideals	165	(16)
VITALI MILMAN
ROY WAGNER
Metric Entropy of the Grassmann Manifold	181	(8)
ALAIN PAJOR
Curvature of Nonlocal Markov Generators	189	(10)
MICHAEL SCHMUCKENSCHLAGER
An Extremal Property of the Regular Simplex	199	(4)
MICHAEL SCHMUCKENSCHLAGER
Floating Body, Illumination Body, and Polytopal Approximation	203	(28)
CARSTEN SCHUTT
A Note on the M* -Limiting Convolution Body	231
ANTONIS TSOLOMITIS