Convex bodies : the Brunn-Minkowski theory
著者
書誌事項
Convex bodies : the Brunn-Minkowski theory
（Encyclopedia of mathematics and its applications / edited by G.-C. Rota, v. 44）
Cambridge University Press, 2008, c1993
- : pbk
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注記
"This digitally printed version 2008" --T.p. verso
Includes bibliographical references and indexes
内容説明・目次
内容説明
At the heart of this monograph is the Brunn-Minkowski theory. It can be used to great effect in studying such ideas as volume and surface area and the generalizations of these. In particular the notions of mixed volume and mixed area arise naturally and the fundamental inequalities that are satisfied by mixed volumes are considered in detail. The author presents a comprehensive introduction to convex bodies and gives full proofs for some deeper theorems. Many hints and pointers to connections with other fields are given, and an exhaustive reference list is included.
目次
- 1. Basic convexity
- 2. Boundary structure
- 3. Minkowski addition
- 4. Curvature measure and quermass integrals
- 5. Mixed volumes
- 6. Inequalities for mixed volumes
- 7. Selected applications
- Appendix.
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