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.

Author: Rolf Schneider
Binding Type: Hardcover
Publisher: Cambridge University Press
Published: 12/09/2013
Series: Encyclopedia of Mathematics and Its Applications #151
Pages: 760
Weight: 2.85lbs
Size: 9.30h x 6.40w x 1.80d
ISBN: 9781107601017
2nd Revised Edition

About the Author
Schneider, Rolf: - Rolf Schneider is Professor Emeritus in the Faculty of Mathematics and Physics at Albert-Ludwigs-Universität Freiburg, Germany.