Existence of infinitely many minimal hypersurfaces in closed manifolds

Antoine Song

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arXiv · 1806.08816

Existence of infinitely many minimal hypersurfaces in closed manifolds

Antoine Song

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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.

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BibTeX RIS

Antoine Song. 2018-06-22. Existence of infinitely many minimal hypersurfaces in closed manifolds. https://arxiv.org/abs/1806.08816

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