Convex bodies : the Brunn-Minkowski theory / Rolf Schneider, Albert-Ludwigs-Universitat Freiburg, Germany.

Format:

Book

Author/Creator:

Schneider, Rolf, 1940- author.

Series:

Encyclopedia of mathematics and its applications ; v. 151.

Encyclopedia of mathematics and its applications ; volume 151

Language:

English

Subjects (All):

Convex bodies.

Physical Description:

1 online resource (xxii, 736 pages) : digital, PDF file(s).

Edition:

Second edition.

Place of Publication:

Cambridge : Cambridge University Press, 2014.

Language Note:

English

Summary:

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.

Contents:

Basic convexity

Boundary structure

Minkowski addition

Support measures and intrinsic volumes

Mixed volumes and related concepts

Valuations on convex bodies

Inequalities for mixed volumes

Determination by area measures and curvatures

Extensions and analogues of the Brunn

Minkowski theory

Affine constructions and inequalities.

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references and indexes.

ISBN:

1-107-45500-6

1-107-46205-3

1-107-45983-4

1-107-46906-6

1-107-46552-4

1-107-47267-9

1-139-00385-2

OCLC:

913796948