Inequalities for quermassintegrals on k-convex domains

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In this paper, we study the Aleksandrov-Fenchel inequalities for quermassintegrals on a class of non-convex domains. Our proof uses optimal transport maps as a tool to relate curvature quantities of different orders defined on the boundary of the domain.

Original languageEnglish (US)
Pages (from-to)335-377
Number of pages43
JournalAdvances in Mathematics
StatePublished - Nov 25 2013

All Science Journal Classification (ASJC) codes

  • General Mathematics


  • Aleksandrov-Fenchel quermassintegral inequalities
  • K-Convexity
  • Optimal transport maps


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