Existence of infinitely many minimal hypersurfaces in closed manifolds

DOI10.4007/ANNALS.2023.197.3.1arXiv1806.08816MaRDI QIDQ6303389

Publication date: 22 June 2018

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.

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)

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