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How to recognize convexity of a set from its marginals

Author(s)
Figalli, Alessio; Jerison, David
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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.
Date issued
2013-06
URI
http://hdl.handle.net/1721.1/102161
Department
Massachusetts Institute of Technology. Department of Mathematics
Journal
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

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