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

© 2022 Annals of Mathematics. 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 [47] and [5]. I would like to thank André Neves for many valuable conversations.

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© 2022 Annals of Mathematics. 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 [47] and [5]. I would like to thank André Neves for many valuable conversations.