How to recognize convexity of a set from its marginals |
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| Authors: | Alessio Figalli David Jerison |
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| Institution: | 1. The University of Texas at Austin, Mathematics Dept. RLM 8.100, 2515 Speedway Stop C1200, Austin, TX 78712-1202, USA;2. Massachusetts Institute of Technology, 77 Massachusetts Ave, Room 2-247, Cambridge, MA 02139-4307, USA |
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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. |
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| Keywords: | Marginals Convexity Log-concavity |
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