Schneider, Rolf creator author. text enk 2013 2nd ed. monographic eng

electronic

1 online resource (760 pages) : digital, PDF file(s). 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. Rolf Schneider. Title from publisher's bibliographic system (viewed on 09 Oct 2015). Convex bodies QA649 .S353 2014 516.3/74 9781139003858 (ebook) http://dx.doi.org/10.1017/CBO9781139003858 http://dx.doi.org/10.1017/CBO9781139003858 UkCbUP 110124 20180107143414.0 CR9781139003858