How to recognize convexity of a set from its marginals
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 fr...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
Elsevier
2016
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| Online Access: | http://hdl.handle.net/1721.1/102161 https://orcid.org/0000-0002-9357-7524 |
| Summary: | 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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