02235nam a22003498a 4500001001600000003000700016005001700023006001900040007001500059008004100074020002600115020002900141040002400170050002300194082001700217100003000234245008900264250001200353264005200365300005900417336002600476337002600502338003600528490006400564500007300628520097600701650001801677776003501695830006501730856007101795999001901866CR9781139003858UkCbUP20180107143414.0m|||||o||d||||||||cr||||||||||||110124s2013||||enk     s     ||1 0|eng|d  a9781139003858 (ebook)  z9781107601017 (hardback)  aUkCbUPcUkCbUPerda00aQA649 b.S353 201400a516.3/742231 aSchneider, Rolf,eauthor.10aConvex Bodies: The Brunn–Minkowski Theory / [electronic resource]cRolf Schneider.  a2nd ed. 1aCambridge :bCambridge University Press,c2013.  a1 online resource (760 pages) :bdigital, PDF file(s).  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier0 aEncyclopedia of Mathematics and its Applications ;vno. 151  aTitle from publisher's bibliographic system (viewed on 09 Oct 2015).  aAt 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. 0aConvex bodies08iPrint version: z9781107601017 0aEncyclopedia of Mathematics and its Applications ;vno. 151.40uhttp://dx.doi.org/10.1017/CBO9781139003858zCambridge Books Online  c236644d236644