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.
General
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