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Convex Geometric Analysis

Convex Geometric Analysis

AUD$56.95 inc GST

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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  • 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.

    • 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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    Reviews & endorsements

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

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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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