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Book Review

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Book Information:

Author: Rolf Schneider
Title: Convex bodies: The Brunn-Minkowski theory
Additional book information: Encyclopedia of Mathematics and its Applications, vol. 44, Cambridge Univ. Press, Cambridge, 1993, xiii + 490 pp., US$89.95. ISBN 0-521-35220-7.

References [Enhancements On Off] (What's this?)

  • [Br1] H. Brunn, Über Ovale und Eiflächen, Dissertation, München, 1887.
  • [Br2] -, Referat über eine Arbeit: Exacte Grundlageg für einer Theorie der Ovale, (S.B. Bayer, ed.), Akad. Wiss., 1894, pp. 93-111.
  • [BZ] Yu. D. Burago and V. A. Zalgaller, Geometric inequalities, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 285, Springer-Verlag, Berlin, 1988. Translated from the Russian by A. B. Sosinskiĭ; Springer Series in Soviet Mathematics. MR 936419
  • [Lus] L.A. Lusternik, Die Brunn-Minkowskische Ungeleichung für beliebige messbare Mengen, Dokl. Acad. Sci. USSR 8 (1935), 55-58.
  • [Min1] H. Minkowski, Theorie der konvexen Körper, insbesondere Begründung ihres Oberflächenbegriffs, Ges. Abh., vol. 2, Teubner, Leipzig, 1911, pp. 131-229.
  • [Min2] -, Geometrie der Zahlen, Teubner, Leipzig, 1910.
  • [MSch] Vitali D. Milman and Gideon Schechtman, Asymptotic theory of finite-dimensional normed spaces, Lecture Notes in Mathematics, vol. 1200, Springer-Verlag, Berlin, 1986. With an appendix by M. Gromov. MR 856576
  • [P] Gilles Pisier, The volume of convex bodies and Banach space geometry, Cambridge Tracts in Mathematics, vol. 94, Cambridge University Press, Cambridge, 1989. MR 1036275
  • [T-J] Nicole Tomczak-Jaegermann, Banach-Mazur distances and finite-dimensional operator ideals, Pitman Monographs and Surveys in Pure and Applied Mathematics, vol. 38, Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, 1989. MR 993774

Review Information:

Reviewer: V. Milman
Journal: Bull. Amer. Math. Soc. 32 (1995), 261-264
DOI: https://doi.org/10.1090/S0273-0979-1995-00581-1