How to recognize convexity of a set from its marginals
Metric Geometry
2015-02-24 v1 Functional Analysis
Abstract
We investigate the regularity of the marginals onto hyperplanes for sets of finite perimeter. We prove, in particular, that if a set of finite perimeter has log-concave marginals onto a.e. hyperplane then the set is convex.
Cite
@article{arxiv.1502.06511,
title = {How to recognize convexity of a set from its marginals},
author = {Alessio Figalli and David Jerison},
journal= {arXiv preprint arXiv:1502.06511},
year = {2015}
}