arXiv Analytics

Sign in

arXiv:1806.08816 [math.DG]AbstractReferencesReviewsResources

Existence of infinitely many minimal hypersurfaces in closed manifolds

Antoine Song

Published 2018-06-22Version 1

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.

Comments: 34 pages
Categories: math.DG, math.AP, math.GT
Related articles: Most relevant | Search more
arXiv:1405.4412 [math.DG] (Published 2014-05-17, updated 2014-05-20)
The Paneitz-Sobolev constant of a closed Riemannian manifold and an application to the nonlocal $\mathbf{Q}$-curvature flow
arXiv:1901.01173 [math.DG] (Published 2019-01-04)
On the Multiplicity One Conjecture in Min-max theory
arXiv:2402.04521 [math.DG] (Published 2024-02-07)
Mean curvature flow with multiplicity $2$ convergence in closed manifolds

Links

Toolbox