Published October 26, 2022
| Accepted Version
Report
Open
Existence of infinitely many minimal hypersurfaces in closed manifolds
- Creators
- Song, Antoine
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.
Additional Information
Attribution 4.0 International (CC BY 4.0) 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.Attached Files
Accepted Version - 1806.08816.pdf
Files
1806.08816.pdf
Files
(384.7 kB)
| Name | Size | Download all |
|---|---|---|
|
md5:1452317d8adb4f045057424f67ee576c
|
384.7 kB | Preview Download |
Additional details
- Eprint ID
- 117597
- Resolver ID
- CaltechAUTHORS:20221026-539144000.10
- DMS-1509027
- NSF
- Created
-
2022-10-26Created from EPrint's datestamp field
- Updated
-
2023-05-03Created from EPrint's last_modified field