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Existence of infinitely many minimal hypersurfaces in closed manifolds

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 (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20221026-539144000.10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)
Related URLs:
URLURL TypeDescription
https://doi.org/10.48550/arXiv.1806.08816DOIDiscussion Paper
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.
Funders:
Funding AgencyGrant Number
NSFDMS-1509027
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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