Accepted Paper
(2010)
Journal: Invent. Math.
Keywords:
Sets of finite perimeter, Mass transportation, isoperimetric inequality, wulff shape
Abstract.
A sharp quantitative version of the anisotropic isoperimetric inequality is established, corresponding to a stability estimate for the Wulff shape of a given surface tension energy. This is achieved by exploiting mass transportation theory, especially Gromov's proof of the isoperimetric inequality and the Brenier-McCann Theorem. A sharp quantitative version of the Brunn-Minkowski inequality for convex sets is proved as a corollary.
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