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.
Recommended Citation
Gardner, Richard J., "The Brunn-Minkowski Inequality" (2002). Mathematics Faculty Publications. 21.
https://cedar.wwu.edu/math_facpubs/21
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
