Existence of infinitely many minimal hypersurfaces in closed manifolds
Differential Geometry
2023-02-17 v2 Analysis of PDEs
Geometric Topology
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.
Cite
@article{arxiv.1806.08816,
title = {Existence of infinitely many minimal hypersurfaces in closed manifolds},
author = {Antoine Song},
journal= {arXiv preprint arXiv:1806.08816},
year = {2023}
}
Comments
v2: small corrections added, references updated, to appear in Ann. of Math