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.
Rezensionen / Stimmen
"A replacement for Bonnesen and Fenchel's text has been very much needed; the monograph under review provides a most satisfactory one." W.J. Firey, Mathematical Reviews
Reihe
Sprache
Verlagsort
Zielgruppe
Maße
Höhe: 241 mm
Breite: 162 mm
Dicke: 32 mm
Gewicht
ISBN-13
978-0-521-35220-8 (9780521352208)
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Schweitzer Klassifikation
Autor*in
Albert-Ludwigs-Universitaet Freiburg, Germany
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.
