The Brunn-Minkowski inequality
Author:
R. J. Gardner
Journal:
Bull. Amer. Math. Soc. 39 (2002), 355-405
MSC (2000):
Primary 26D15, 52A40
DOI:
https://doi.org/10.1090/S0273-0979-02-00941-2
Published electronically:
April 8, 2002
MathSciNet review:
1898210
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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 , 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.
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Additional Information
R. J. Gardner
Affiliation:
Department of Mathematics, Western Washington University, Bellingham, Washington 98225-9063
Email:
gardner@baker.math.wwu.edu
DOI:
https://doi.org/10.1090/S0273-0979-02-00941-2
Keywords:
Brunn-Minkowski inequality,
Minkowski's first inequality,
Pr\'{e}kopa-Leindler inequality,
Young's inequality,
Brascamp-Lieb inequality,
Barthe's inequality,
isoperimetric inequality,
Sobolev inequality,
entropy power inequality,
covariogram,
Anderson's theorem,
concave function,
concave measure,
convex body,
mixed volume
Received by editor(s):
February 1, 2001
Received by editor(s) in revised form:
November 28, 2001
Published electronically:
April 8, 2002
Additional Notes:
Supported in part by NSF Grant DMS 9802388.
Article copyright:
© Copyright 2002
American Mathematical Society