A mass transportation approach to quantitative isoperimetric inequalities

• 成果类型: Article
• 署名作者: Figalli, A.; Maggi, F.; Pratelli, A.
• 署名单位: University of Texas System; University of Texas Austin; University of Florence; University of Pavia
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-010-0261-z
• 发表日期: 2010
• 页码: 167-211
• 关键词: sobolev inequality; sharp sobolev; minkowski; uniqueness; STABILITY; surface; THEOREM

摘要

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.