Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4590547 | Journal of Functional Analysis | 2014 | 17 Pages |
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. Our proof relies on measuring the perimeter of a set through a Hilbertian fractional Sobolev norm, a fact that we believe has its own interest.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Alessio Figalli, David Jerison,