Some higher order isoperimetric inequalities via the method of optimal transport

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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 languageEnglish (US)
Pages (from-to)6619-6644
Number of pages26
JournalInternational Mathematics Research Notices
Volume2014
Issue number24
DOIs
StatePublished - Jan 1 2014

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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