Existence of infinitely many minimal hypersurfaces in closed manifolds

By Antoine Song. Annals of Mathematics, 2018

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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.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/3ac50b85033eedad0c4650ff7a845bb0dcc5a873