Existence of infinitely many minimal hypersurfaces in closed manifolds

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.

v2: small corrections added, references updated, to appear in Ann. of Math

References in corpus (1)

• On the existence of minimal Heegaard surfaces

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