02235nam a22003498a 4500 CR9781139003858 UkCbUP 20180107143414.0 m|||||o||d|||||||| cr|||||||||||| 110124s2013||||enk s ||1 0|eng|d 9781139003858 (ebook) 9781107601017 (hardback) UkCbUP UkCbUP rda QA649 .S353 2014 516.3/74 23 Schneider, Rolf, author. Convex Bodies: The Brunn–Minkowski Theory / [electronic resource] Rolf Schneider. 2nd ed. Cambridge : Cambridge University Press, 2013. 1 online resource (760 pages) : digital, PDF file(s). text txt rdacontent computer c rdamedia online resource cr rdacarrier Encyclopedia of Mathematics and its Applications ; no. 151 Title from publisher's bibliographic system (viewed on 09 Oct 2015). 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. Convex bodies Print version: 9781107601017 Encyclopedia of Mathematics and its Applications ; no. 151. http://dx.doi.org/10.1017/CBO9781139003858 Cambridge Books Online 236644 236644