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 $k$-th 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.

21 pages

References in corpus (2)

• On asymptotically harmonic manifolds of negative curvature
• Submanifolds, Isoperimetric Inequalities and Optimal Transportation

Cited by in corpus (2)

• Alexandrov-Fenchel inequality for convex hypersurfaces with capillary boundary in a ball
• Classical Neumann Problems for Hessian equations and Alexandrov-Fenchel's inequalities