TY - BOOK AU - Schneider,Rolf TI - Convex bodies: the Brunn-Minkowski theory T2 - Encyclopedia of mathematics and its applications SN - 9781107601017 (hardback) U1 - 516.374 23 PY - 2014/// CY - Cambridge PB - CUP KW - Convex bodies N1 - "First published 1993; first paperback edition 2008"--Title page verso; Includes bibliographical references (pages 629-714) and indexes; 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-- N2 - A complete presentation of a central part of convex geometry, from basics for beginners, to the exposition of current research ER -