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.
A mass transportation approach to quantitative isoperimetric inequalities / A. Figalli; F. Maggi; A. Pratelli. - In: INVENTIONES MATHEMATICAE. - ISSN 0020-9910. - STAMPA. - 182(2010), pp. 167-211.
Titolo: | A mass transportation approach to quantitative isoperimetric inequalities | |
Autori di Ateneo: | ||
Autori: | A. Figalli; MAGGI, FRANCESCO; A. Pratelli | |
Data di pubblicazione: | 2010 | |
Rivista: | ||
Volume: | 182 | |
Pagina iniziale: | 167 | |
Pagina finale: | 211 | |
Abstract: | 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. | |
Handle: | http://hdl.handle.net/2158/389955 | |
Appare nelle tipologie: | 1a - Articolo su rivista |
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Figalli Maggi Pratelli A mass transportation approach to (10).pdf | Versione finale referata (Postprint, Accepted manuscript) | DRM non definito | Administrator |