How to recognize convexity of a set from its marginals
Author(s)
Figalli, Alessio; Jerison, David
Download2016_Jerison_How to recognize.pdf (192.5Kb)
PUBLISHER_CC
Publisher with Creative Commons License
Creative Commons Attribution
Terms of use
Metadata
Show full item recordAbstract
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.
Date issued
2013-06Department
Massachusetts Institute of Technology. Department of MathematicsJournal
Journal of Functional Analysis
Publisher
Elsevier
Citation
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.
Version: Author's final manuscript
ISSN
00221236
1096-0783