Min-max theory for constant mean curvature hypersurfaces

Abstract

In this paper, we develop a min-max theory for the construction of constant mean curvature (CMC) hypersurfaces of prescribed mean curvature in an arbitrary closed manifold. As a corollary, we prove the existence of a nontrivial, smooth, closed, almost embedded, CMC hypersurface of any given mean curvature $c$. Moreover, if $c$ is nonzero then our min-max solution always has multiplicity one.

arXiv comment32 pages. More backgrounds and references added. Comments welcome!

References in corpus (5)

• Min-max theory for free boundary minimal hypersurfaces I - regularity theory
• Equivariant min-max theory
• Degree Theory of Immersed Hypersurfaces
• Entropy of closed surfaces and min-max theory
• Local min-max surfaces and strongly irreducible minimal Heegaard splittings

Cited by in corpus (5)

• Compactness and generic finiteness for free boundary minimal hypersurfaces (I)
• Existence of hypersurfaces with prescribed mean curvature I - Generic min-max
• Compactness of Constant Mean Curvature Surfaces in Three Manifold with Positive Ricci Curvature
• Min-max theory for networks of constant geodesic curvature
• Constant Mean Curvature Surfaces in Homology Classes