A mass transportation approach to quantitative isoperimetric inequalities
Figalli A, Maggi F, Pratelli A (2010)
Publication Language: English
Publication Status: Published
Publication Type: Journal article
Publication year: 2010
Journal
Publisher: Springer Verlag (Germany)
Book Volume: 182
Pages Range: 167-211
Journal Issue: 1
DOI: 10.1007/s00222-010-0261-z
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.
Authors with CRIS profile
Involved external institutions
University of Texas at Austin
United States (USA) (US)
Università degli Studi di Firenze / University of Florence
Italy (IT)
United States (USA) (US)
Università degli Studi di Firenze / University of Florence
Italy (IT)
How to cite
APA:
Figalli, A., Maggi, F., & Pratelli, A. (2010). A mass transportation approach to quantitative isoperimetric inequalities. Inventiones Mathematicae, 182(1), 167-211. https://dx.doi.org/10.1007/s00222-010-0261-z
MLA:
Figalli, Alessio, Francesco Maggi, and Aldo Pratelli. "A mass transportation approach to quantitative isoperimetric inequalities." Inventiones Mathematicae 182.1 (2010): 167-211.
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