Convex Bodies
The Brunn-Minkowski Theory
Seiten
2008
Cambridge University Press (Verlag)
978-0-521-05991-6 (ISBN)
Cambridge University Press (Verlag)
978-0-521-05991-6 (ISBN)
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The author presents a comprehensive introduction to convex bodies and gives full proofs for some deeper theorems which have never previously been brought together. Many hints and pointers to connections with other fields are given, and an exhaustive reference list is included.
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.
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.
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.
| Erscheint lt. Verlag | 18.2.2008 |
|---|---|
| Reihe/Serie | Encyclopedia of Mathematics and its Applications |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 713 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| ISBN-10 | 0-521-05991-7 / 0521059917 |
| ISBN-13 | 978-0-521-05991-6 / 9780521059916 |
| Zustand | Neuware |
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