Convex Bodies

The Brunn-Minkowski Theory
Erscheinungsjahr 1993
ISBN: 978-0-521-35220-8
Verlag: Cambridge University Press

Buch, Englisch, 504 Seiten, Format (B × H): 156 mm x 234 mm, Gewicht: 916 g

Reihe: Encyclopedia of Mathematics and Its Applications

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.

Autoren/Hrsg.

Schneider, Rolf

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie

Inhaltsverzeichnis

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.