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.
Antoine Song. "Existence of infinitely many minimal hypersurfaces in closed manifolds." Ann. of Math. (2) 197 (3) 859 - 895, May 2023. https://doi.org/10.4007/annals.2023.197.3.1