Convex Bodies: The Brunn–Minkowski Theory
Seiten
2013
|
2nd Revised edition
Cambridge University Press (Verlag)
978-1-107-60101-7 (ISBN)
Cambridge University Press (Verlag)
978-1-107-60101-7 (ISBN)
Now in its second edition, this classic text has been expanded to reflect significant developments in Brunn–Minkowski theory over the past two decades. It gives a complete presentation from basics to the exposition of current research, with full proofs, pointers to other fields and a fully updated reference list.
At the heart of this monograph is the Brunn–Minkowski theory, which can be used to great effect in studying such ideas as volume and surface area and their generalizations. In particular, the notions of mixed volume and mixed area measure arise naturally and the fundamental inequalities that are satisfied by mixed volumes are considered here in detail. The author presents a comprehensive introduction to convex bodies, including full proofs for some deeper theorems. The book provides hints and pointers to connections with other fields and an exhaustive reference list. This second edition has been considerably expanded to reflect the rapid developments of the past two decades. It includes new chapters on valuations on convex bodies, on extensions like the Lp Brunn–Minkowski theory, and on affine constructions and inequalities. There are also many supplements and updates to the original chapters, and a substantial expansion of chapter notes and references.
At the heart of this monograph is the Brunn–Minkowski theory, which can be used to great effect in studying such ideas as volume and surface area and their generalizations. In particular, the notions of mixed volume and mixed area measure arise naturally and the fundamental inequalities that are satisfied by mixed volumes are considered here in detail. The author presents a comprehensive introduction to convex bodies, including full proofs for some deeper theorems. The book provides hints and pointers to connections with other fields and an exhaustive reference list. This second edition has been considerably expanded to reflect the rapid developments of the past two decades. It includes new chapters on valuations on convex bodies, on extensions like the Lp Brunn–Minkowski theory, and on affine constructions and inequalities. There are also many supplements and updates to the original chapters, and a substantial expansion of chapter notes and references.
Rolf Schneider is Professor Emeritus in the Faculty of Mathematics and Physics at Albert-Ludwigs-Universität Freiburg, Germany.
Preface to the second edition; Preface to the first edition; General hints to the literature; Conventions and notation; 1. Basic convexity; 2. Boundary structure; 3. Minkowski addition; 4. Support measures and intrinsic volumes; 5. Mixed volumes and related concepts; 6. Valuations on convex bodies; 7. Inequalities for mixed volumes; 8. Determination by area measures and curvatures; 9. Extensions and analogues of the Brunn–Minkowski theory; 10. Affine constructions and inequalities; Appendix. Spherical harmonics; References; Notation index; Author index; Subject index.
| Reihe/Serie | Encyclopedia of Mathematics and its Applications |
|---|---|
| Verlagsort | Cambridge |
| Sprache | englisch |
| Maße | 163 x 236 mm |
| Gewicht | 1290 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| ISBN-10 | 1-107-60101-0 / 1107601010 |
| ISBN-13 | 978-1-107-60101-7 / 9781107601017 |
| Zustand | Neuware |
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