Some higher order isoperimetric inequalities via the method of optimal transport
classification
🧮 math.DG
math.AP
keywords
inequalitiesconvexdomainsmethodoptimalsomealexandrov-fenchelclassical
read the original 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.
This paper has not been read by Pith yet.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.