Book Review
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MathSciNet review:
1568169
Full text of 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.
[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.
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, DOI 10.1007/978-3-662-07441-1
[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.
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
Gilles Pisier, The volume of convex bodies and Banach space geometry, Cambridge Tracts in Mathematics, vol. 94, Cambridge University Press, Cambridge, 1989. MR 1036275, DOI 10.1017/CBO9780511662454
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
- [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, Geometrie inequalities, Grundlehren Math. Wiss., Springer-Verlag, Berlin, 1988, pp. 285. MR 936419 (89b:52020)
- [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]
- V.D. Milman and G. Schechtman, Asymptotic theory of finite dimensional normed spaces, Lecture Notes in Math., vol. 1200, Springer, New York, 1986. MR 856576 (87m:46038)
- [P]
- G. Pisier, The volume of convex bodies and Banach space geometry, Cambridge Univ. Press, Cambridge, 1989. MR 1036275 (91d:52005)
- [T-J]
- N. Tomczak-Jaegermann, Banach-Mazur distances and finite dimensional operator ideals, Pitman Monographs, vol. 38, Longman Scientific & Technical, New York and London, 1989. MR 993774 (90k:46039)
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
