Existence of minimal hypersurfaces in complete manifolds of finite volume
We prove that every complete non-compact manifold of finite volume contains a (possibly non-compact) minimal hypersurface of finite volume. The main tool is the following result of independent interest: if a region U can be swept out by a family of hypersurfaces of volume at most V, then it can be s...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Springer Berlin Heidelberg
2020
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| Online Access: | https://hdl.handle.net/1721.1/128678 |
| _version_ | 1811076084512325632 |
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| author | Chambers, Gregory R Liokumovich, Yevgeniy |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Chambers, Gregory R Liokumovich, Yevgeniy |
| author_sort | Chambers, Gregory R |
| collection | MIT |
| description | We prove that every complete non-compact manifold of finite volume contains a (possibly non-compact) minimal hypersurface of finite volume. The main tool is the following result of independent interest: if a region U can be swept out by a family of hypersurfaces of volume at most V, then it can be swept out by a family of mutually disjoint hypersurfaces of volume at most V+ε. |
| first_indexed | 2024-09-23T10:15:55Z |
| format | Article |
| id | mit-1721.1/128678 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T10:15:55Z |
| publishDate | 2020 |
| publisher | Springer Berlin Heidelberg |
| record_format | dspace |
| spelling | mit-1721.1/1286782022-09-30T20:00:38Z Existence of minimal hypersurfaces in complete manifolds of finite volume Chambers, Gregory R Liokumovich, Yevgeniy Massachusetts Institute of Technology. Department of Mathematics We prove that every complete non-compact manifold of finite volume contains a (possibly non-compact) minimal hypersurface of finite volume. The main tool is the following result of independent interest: if a region U can be swept out by a family of hypersurfaces of volume at most V, then it can be swept out by a family of mutually disjoint hypersurfaces of volume at most V+ε. 2020-11-30T15:58:14Z 2020-11-30T15:58:14Z 2020-08 2020-09-24T20:53:24Z Article http://purl.org/eprint/type/JournalArticle 0020-9910 1432-1297 https://hdl.handle.net/1721.1/128678 Chambers, Gregory R., and Yevgeniy Liokumovich, "Existence of minimal hypersurfaces in complete manifolds of finite volume." Inventiones mathematicae 219 (2020): 179-217 ©2020 Author(s) en 10.1007/s00222-019-00903-3 Inventiones mathematicae Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. Springer-Verlag GmbH Germany, part of Springer Nature application/pdf Springer Berlin Heidelberg Springer Berlin Heidelberg |
| spellingShingle | Chambers, Gregory R Liokumovich, Yevgeniy Existence of minimal hypersurfaces in complete manifolds of finite volume |
| title | Existence of minimal hypersurfaces in complete manifolds of finite volume |
| title_full | Existence of minimal hypersurfaces in complete manifolds of finite volume |
| title_fullStr | Existence of minimal hypersurfaces in complete manifolds of finite volume |
| title_full_unstemmed | Existence of minimal hypersurfaces in complete manifolds of finite volume |
| title_short | Existence of minimal hypersurfaces in complete manifolds of finite volume |
| title_sort | existence of minimal hypersurfaces in complete manifolds of finite volume |
| url | https://hdl.handle.net/1721.1/128678 |
| work_keys_str_mv | AT chambersgregoryr existenceofminimalhypersurfacesincompletemanifoldsoffinitevolume AT liokumovichyevgeniy existenceofminimalhypersurfacesincompletemanifoldsoffinitevolume |