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The Brunn-Minkowski inequality
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by R. J. Gardner PDF

Bull. Amer. Math. Soc. 39 (2002), 355-405 Request permission

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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The Brunn-Minkowski inequality
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