Convex Bodies: The Brunn-Minkowski Theory

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9780511526282: Convex Bodies: The Brunn-Minkowski Theory

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.

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Recensione:

"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

Descrizione del libro:

The author presents a comprehensive introduction to convex bodies and gives full proofs for some deeper theorems which have never previously been brought together. Many hints and pointers to connections with other fields are given, and an exhaustive reference list is included.

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