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A mass transportation approach to quantitative isoperimetric inequalities |
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| Authors: | A Figalli F Maggi A Pratelli |
| Institution: | 1. Department of Mathematics, The University of Texas at Austin, 1 University Station C1200, Austin, TX, 78712, USA 2. Dipartimento di Matematica “U. Dini”, Università di Firenze, Viale Morgagni 67/A, 50134, Firenze, Italy 3. Dipartimento di Matematica, Università di Pavia, via Ferrata 1, 27100, Pavia, Italy |
| 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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