Convex Bodies

At the heart of this monograph is the BrunnMinkowski 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 BrunnMinkowski 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.