Some higher order isoperimetric inequalities via the method of optimal transport

Sun Yung A. Chang; Yi Wang

doi:10.1093/imrn/rnt182

Some higher order isoperimetric inequalities via the method of optimal transport

Sun Yung A. Chang, Yi Wang

Mathematics

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

In this paper, we establish some sharp inequalities between the volume and the integral of the kth mean curvature for (k+1)-convex domains in the Euclidean space. The results generalize the classical Alexandrov-Fenchel inequalities for convex domains. Our proof utilizes the method of optimal transportation.

Original language	English (US)
Pages (from-to)	6619-6644
Number of pages	26
Journal	International Mathematics Research Notices
Volume	2014
Issue number	24
DOIs	https://doi.org/10.1093/imrn/rnt182
State	Published - Jan 1 2014

All Science Journal Classification (ASJC) codes

General Mathematics

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title = "Some higher order isoperimetric inequalities via the method of optimal transport",

abstract = "In this paper, we establish some sharp inequalities between the volume and the integral of the kth mean curvature for (k+1)-convex domains in the Euclidean space. The results generalize the classical Alexandrov-Fenchel inequalities for convex domains. Our proof utilizes the method of optimal transportation.",

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AB - In this paper, we establish some sharp inequalities between the volume and the integral of the kth mean curvature for (k+1)-convex domains in the Euclidean space. The results generalize the classical Alexandrov-Fenchel inequalities for convex domains. Our proof utilizes the method of optimal transportation.

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Some higher order isoperimetric inequalities via the method of optimal transport

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