Existence of minimal surfaces of arbitrarily large Morse index
We show that in a closed 3-manifold with a generic metric of positive Ricci curvature, there are minimal surfaces of arbitrary large Morse index, which partially confirms a conjecture by Marques and Neves. We prove this by analyzing the lamination structure of the limit of minimal surfaces with boun...
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| Format: | Article |
| Language: | English |
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Springer Berlin Heidelberg
2017
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| Online Access: | http://hdl.handle.net/1721.1/107182 https://orcid.org/0000-0002-0212-4504 |
| _version_ | 1826217580644270080 |
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| author | Li, Haozhao Zhou, Xin |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Li, Haozhao Zhou, Xin |
| author_sort | Li, Haozhao |
| collection | MIT |
| description | We show that in a closed 3-manifold with a generic metric of positive Ricci curvature, there are minimal surfaces of arbitrary large Morse index, which partially confirms a conjecture by Marques and Neves. We prove this by analyzing the lamination structure of the limit of minimal surfaces with bounded Morse index. |
| first_indexed | 2024-09-23T17:05:56Z |
| format | Article |
| id | mit-1721.1/107182 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T17:05:56Z |
| publishDate | 2017 |
| publisher | Springer Berlin Heidelberg |
| record_format | dspace |
| spelling | mit-1721.1/1071822022-10-03T10:23:56Z Existence of minimal surfaces of arbitrarily large Morse index Li, Haozhao Zhou, Xin Massachusetts Institute of Technology. Department of Mathematics Zhou, Xin We show that in a closed 3-manifold with a generic metric of positive Ricci curvature, there are minimal surfaces of arbitrary large Morse index, which partially confirms a conjecture by Marques and Neves. We prove this by analyzing the lamination structure of the limit of minimal surfaces with bounded Morse index. National Natural Science Foundation (China) (Grant No. 11131007) National Science Foundation (U.S.) (Grant DMS-1406337) 2017-03-04T00:12:50Z 2017-03-04T00:12:50Z 2016-05 2015-04 2017-02-02T15:20:26Z Article http://purl.org/eprint/type/JournalArticle 0944-2669 1432-0835 http://hdl.handle.net/1721.1/107182 Li, Haozhao, and Xin Zhou. “Existence of Minimal Surfaces of Arbitrarily Large Morse Index.” Calculus of Variations and Partial Differential Equations 55.3 (2016): n. pag. https://orcid.org/0000-0002-0212-4504 en http://dx.doi.org/10.1007/s00526-016-1007-6 Calculus of Variations and Partial Differential Equations 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 Berlin Heidelberg application/pdf Springer Berlin Heidelberg Springer Berlin Heidelberg |
| spellingShingle | Li, Haozhao Zhou, Xin Existence of minimal surfaces of arbitrarily large Morse index |
| title | Existence of minimal surfaces of arbitrarily large Morse index |
| title_full | Existence of minimal surfaces of arbitrarily large Morse index |
| title_fullStr | Existence of minimal surfaces of arbitrarily large Morse index |
| title_full_unstemmed | Existence of minimal surfaces of arbitrarily large Morse index |
| title_short | Existence of minimal surfaces of arbitrarily large Morse index |
| title_sort | existence of minimal surfaces of arbitrarily large morse index |
| url | http://hdl.handle.net/1721.1/107182 https://orcid.org/0000-0002-0212-4504 |
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