Song, Antoine (2018) Existence of infinitely many minimal hypersurfaces in closed manifolds. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20221026-539144000.10
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Abstract
Using min-max theory, we show that in any closed Riemannian manifold of dimension at least 3 and at most 7, there exist infinitely many smoothly embedded closed minimal hypersurfaces. It proves a conjecture of S.-T. Yau. This paper builds on the methods developed by F. C. Marques and A. Neves.
| Item Type: | Report or Paper (Discussion Paper) | ||||||
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| Additional Information: | The author was partially supported by NSF-DMS-1509027. I am very grateful to my advisor Fernando Codá Marques for his constant support, his generosity and inspiring discussions during the course of this work. I also thank him for pointing out references [39] and [5]. I would like to thank André Neves for many valuable conversations. | ||||||
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| DOI: | 10.48550/arXiv.1806.08816 | ||||||
| Record Number: | CaltechAUTHORS:20221026-539144000.10 | ||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20221026-539144000.10 | ||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||
| ID Code: | 117597 | ||||||
| Collection: | CaltechAUTHORS | ||||||
| Deposited By: | George Porter | ||||||
| Deposited On: | 26 Oct 2022 23:22 | ||||||
| Last Modified: | 26 Oct 2022 23:22 |
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