Convex Geometric Analysis

Articles on classical convex geometry, geometric functional analysis, computational geometry, and related areas of harmonic analysis, first published in 1999.

Keith M. Ball (Edited by), Vitali Milman (Edited by)

9780521155649, Cambridge University Press

Paperback, published 21 July 2011

258 pages
23.4 x 15.6 x 1.4 cm, 0.37 kg

Review of the hardback: '… a useful source of inspiration for mathematicians working in convex geometry and functional analysis.' European Mathematical Society

Convex geometry is at once simple and amazingly rich. While the classical results go back many decades, during that previous to this book's publication in 1999, the integral geometry of convex bodies had 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.

1. Integrals of smooth and analytic functions over Minkowski's sums of convex sets S. Alesker
2. On the Gromov–Milman theorem on concentration phenomenon on the uniformly convex sphere S. Alesker
3. Geometric inequalities in option pricing Christer Borell
4. Random points in isotropic convex sets Jean Bourgain
5. Threshold intervals under group symmetries Jean Bourgain and G. Kalai
6. On a generalization of the Busemann–Petty problem Jean Bourgain and Gaoyong Zhang
7. Isotropic constants of Schatten class spaces Sean Dar
8. On the stability of the volume radius E. D. Gluskin
9. Polytope approximations of the unit ball of Lpn W. T. Gowers
10. A remark about the scalar-plus-compact problem W. T. Gowers
11. Another low-technology estimate in convex geometry Greg Kuperberg
12. On the equivalence between geometric and arithmetic means for log-concave measures Rafal Latala
13. On the constant in the Reverse Brunn–Minkowski inequality for p-convex balls A. E. Litvak
14. An extension of Krivine's theorem to quasi-normed spaces A. E. Litvak
15. A note on Gowersí dichotomy theorem Bernard Maurey
16. An isomorphic version of Dvoretzky's theorem II Vitali Milman and Gideon Schechtman
17. Asymptotic versions of operators and operator ideals V. Milman and R. Wagner
18. Metric entropy of the Grassman manifold Alain Pajor
19. Curvature of nonlocal Markov generators Michael Schmuckenschlager
20. An external property of the regular simplex Michael Schmuckenschlager
21. Floating body, illumination body, and polytopal approximation Carsten Schutt
22. A note on the M*-limiting convolution body Antonis Tsolomitis.

Subject Areas: Calculus & mathematical analysis [PBK]