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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 (Unpublished)

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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.

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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.
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Record Number:CaltechAUTHORS:20221026-539144000.10
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:117597
Deposited By: George Porter
Deposited On:26 Oct 2022 23:22
Last Modified:03 May 2023 22:34

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