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arXiv · 1707.08012

Min-max theory for constant mean curvature hypersurfaces

Xin Zhou·Jonathan J. Zhu
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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.

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Xin Zhou, Jonathan J. Zhu. 2017-07-25. Min-max theory for constant mean curvature hypersurfaces. https://arxiv.org/abs/1707.08012

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