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Min-max theory for constant mean curvature hypersurfaces

Xin Zhou University of California Santa Barbara Jonathan J. Zhu Princeton University

arXiv subject: Differential Geometry (math.DG) mathscidoc:2005.53001

Gold Award Paper in 2020

Inventiones mathematicae , 218, 441–490, 2019
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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  • https://link.springer.com/article/10.1007/s00222-019-00886-1
@inproceedings{xin2019min-max,
  title={Min-max theory for constant mean curvature hypersurfaces},
  author={Xin Zhou, and Jonathan J. Zhu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20200510223119931862667},
  booktitle={Inventiones mathematicae },
  volume={218},
  pages={441–490},
  year={2019},
}
Xin Zhou, and Jonathan J. Zhu. Min-max theory for constant mean curvature hypersurfaces. 2019. Vol. 218. In Inventiones mathematicae . pp.441–490. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20200510223119931862667.
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