Convex bodies : the Brunn-Minkowski theory
- Rolf Schneider.
- Second expanded edition.
- Cambridge : Cambridge University Press, 2014.
- Physical description
- xxii, 736 pages : illustrations ; 24 cm.
- Encyclopedia of mathematics and its applications ; v. 151.
Math & Statistics Library
QA649 .S353 2014
- Unknown QA649 .S353 2014
- Schneider, Rolf, 1940-
- Includes bibliographical references (pages -714) and indexes.
- Preface to the second edition-- Preface to the first edition-- General hints to the literature-- Conventions and notation-- 1. Basic convexity-- 2. Boundary structure-- 3. Minkowski addition-- 4. Support measures and intrinsic volumes-- 5. Mixed volumes and related concepts-- 6. Valuations on convex bodies-- 7. Inequalities for mixed volumes-- 8. Determination by area measures and curvatures-- 9. Extensions and analogues of the Brunn-Minkowski theory-- 10. Affine constructions and inequalities-- Appendix. Spherical harmonics-- References-- Notation index-- Author index-- Subject index.
- (source: Nielsen Book Data)
- Publisher's Summary
- 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.
(source: Nielsen Book Data)
- Convex bodies.
- Publication date
- Encyclopedia of mathematics and its applications ; v. 151
- "First published 1993; first paperback edition 2008"--Title page verso.
- 9781107601017 (hardback)