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Convex Geometric Analysis

Convex Geometric Analysis

$40.00

Part of Mathematical Sciences Research Institute Publications

S. Alesker, Christer Borell, Jean Bourgain, G. Kalai, Gaoyong Zhang, Sean Dar, E. D. Gluskin, W. T. Gowers, Greg Kuperberg, Rafal Latala, A. E. Litvak, Bernard Maurey, Vitali Milman, Gideon Schechtman, R. Wagner, Alain Pajor, Michael Schmuckenschlager, Carsten Schutt, Antonis Tsolomitis
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  • Date Published: July 2011
  • availability: Available
  • format: Paperback
  • isbn: 9780521155649

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About the Authors
  • Convex bodies are at once simple and amazingly rich in structure. While the classical results go back many decades, during the past 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 collection arises from an MSRI program held in the Spring of 1996, involving researchers in classical convex geometry, geometric functional analysis, computational geometry, and related areas of harmonic analysis. It is representative of the best research in a very active field that brings together ideas from several major strands in mathematics.

    • Top contributors, including Fields medallists
    • Has the best research from a very active field
    • Brings together ideas from several major strands in mathematics
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    Product details

    • Date Published: July 2011
    • format: Paperback
    • isbn: 9780521155649
    • length: 258 pages
    • dimensions: 234 x 156 x 14 mm
    • weight: 0.37kg
    • availability: Available
  • Table of Contents

    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.

  • Editors

    Keith M. Ball, University College London

    Vitali Milman, Tel-Aviv University

    Contributors

    S. Alesker, Christer Borell, Jean Bourgain, G. Kalai, Gaoyong Zhang, Sean Dar, E. D. Gluskin, W. T. Gowers, Greg Kuperberg, Rafal Latala, A. E. Litvak, Bernard Maurey, Vitali Milman, Gideon Schechtman, R. Wagner, Alain Pajor, Michael Schmuckenschlager, Carsten Schutt, Antonis Tsolomitis

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