Convex Bodies: The Brunn–Minkowski Theory: 151 (Encyclopedia of Mathematics and its Applications, Series Number 151) - Hardcover

Schneider, Rolf

Hardcover

ISBN 10: 1107601010 ISBN 13: 9781107601017

Publisher: Cambridge University Press, 2013

Synopsis

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.

About this title

Review:

Review of the first edition: 'Neither one of [the old classics] may be considered a substitute for the excellent detailed monograph written by Rolf Schneider. I recommend this book to everyone who appreciates the beauty of convexity theory or who uses the strength of geometric inequalities, and to any expert who needs a reliable reference book for his/her research.' V. Milman, Bulletin of the American Mathematical Society

Review of the first edition: 'Professor Schneider's book is the first comprehensive account of the Brunn-Minkowski theory and will immediately become the standard reference for the Aleksandrov-Fenchel inequalities and the current knowledge concerning the cases of equality and estimates of their stability. The book is aimed at a broad audience from graduate students to working professionals. The presentation is very clear and I enjoyed reading it.' Bulletin of the London Mathematical Society

Book Description:

Now in its second edition, this classic text has been expanded to reflect significant developments in Brunn–Minkowski theory over the past two decades. It gives a complete presentation from basics to the exposition of current research, with full proofs, pointers to other fields and a fully updated reference list.

About this edition

• Publisher: Cambridge University Press
• Publication date: 2013
• ISBN 10: 1107601010
• ISBN 13: 9781107601017
• Binding: Hardcover
• Edition number: 2
• Number of pages: 760