The Brunn-Minkowski inequality

Gardner, R.

doi:10.1090/S0273-0979-02-00941-2

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

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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 ${\mathbb R}^n$ , 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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