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 |
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Elsevier
2016
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| Online Access: | http://hdl.handle.net/1721.1/102161 https://orcid.org/0000-0002-9357-7524 |
| _version_ | 1826194853585747968 |
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| author | Figalli, Alessio Jerison, David |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Figalli, Alessio Jerison, David |
| author_sort | Figalli, Alessio |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T10:03:12Z |
| format | Article |
| id | mit-1721.1/102161 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T10:03:12Z |
| publishDate | 2016 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | mit-1721.1/1021612022-09-30T18:36:04Z How to recognize convexity of a set from its marginals Figalli, Alessio Jerison, David Massachusetts Institute of Technology. Department of Mathematics Jerison, David 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. National Science Foundation (U.S.) (Grant DMS-1069225) 2016-04-04T23:29:14Z 2016-04-04T23:29:14Z 2013-06 2013-05 Article http://purl.org/eprint/type/JournalArticle 00221236 1096-0783 http://hdl.handle.net/1721.1/102161 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. https://orcid.org/0000-0002-9357-7524 en_US http://dx.doi.org/10.1016/j.jfa.2013.05.040 Journal of Functional Analysis Creative Commons Attribution-Noncommercial-NoDerivatives http://creativecommons.org/licenses/by-nc-nd/4.0/ application/pdf Elsevier Other univ. web domain |
| spellingShingle | Figalli, Alessio Jerison, David How to recognize convexity of a set from its marginals |
| title | How to recognize convexity of a set from its marginals |
| title_full | How to recognize convexity of a set from its marginals |
| title_fullStr | How to recognize convexity of a set from its marginals |
| title_full_unstemmed | How to recognize convexity of a set from its marginals |
| title_short | How to recognize convexity of a set from its marginals |
| title_sort | how to recognize convexity of a set from its marginals |
| url | http://hdl.handle.net/1721.1/102161 https://orcid.org/0000-0002-9357-7524 |
| work_keys_str_mv | AT figallialessio howtorecognizeconvexityofasetfromitsmarginals AT jerisondavid howtorecognizeconvexityofasetfromitsmarginals |