Document Type

Article

Publication Date

2002

Keywords

Brunn-Minkowski inequality, Minkowski’s first inequality, Prekopa-Leindler inequality, Young’s inequality, Brascamp-Lieb inequality, Barthe’s inequality, isoperimetric inequality, Sobolev inequality, entropy power inequality, covariogram, Anderson’s theorem, concave measure, convex body, mixed volume

Abstract

In 1978, Osserman [124] wrote an extensive survey on the isoperimetric inequality. The Brunn-Minkowski inequality can be proved in a page, yet quickly yields the classical isoperimetric inequality for important classes of subsets of Rn, and deserves to be better known. This guide explains the relationship between the Brunn-Minkowski inequality and other inequalities in geometry and analysis, and some applications.

Publication Title

Bulletin of the American Mathematical Society

Volume

39

Issue

3

First Page

355

Last Page

405

Required Publisher's Statement

First published in The Bulletin of the American Mathematical Society in Volume 39, Number 3, published by the American Mathematical Society.

Subjects - Topical (LCSH)

Convex domains; Concave functions; Convex bodies

Genre/Form

articles

Type

Text

Rights

Copying of this document in whole or in part is allowable only for scholarly purposes. It is understood, however, that any copying or publication of this document for commercial purposes, or for financial gain, shall not be allowed without the author’s written permission.

Language

English

Format

application/pdf

Included in

Mathematics Commons

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