How to recognize convexity of a set from its marginals
Author(s)Figalli, Alessio; Jerison, David
MetadataShow full item record
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.
DepartmentMassachusetts Institute of Technology. Department of Mathematics
Journal of Functional Analysis
Figalli, Alessio, and David Jerison. “How to Recognize Convexity of a Set from Its Marginals.” Journal of Functional Analysis 266, no. 3 (February 2014): 1685–1701.
Author's final manuscript