Min-max theory for constant mean curvature hypersurfaces

被引：37
作者：
Zhou, Xin [1 ,3 ]
Zhu, Jonathan J. [2 ]
机构：
[1] Univ Calif Santa Barbara, Dept Math, Santa Barbara, CA 93106 USA
[2] Harvard Univ, Dept Math, Cambridge, MA 02138 USA
[3] Princeton Univ, Dept Math, Princeton, NJ 08544 USA
来源：
INVENTIONES MATHEMATICAE | 2019年 / 218卷 / 02期
关键词：
MINIMAL HYPERSURFACES; SURFACES; EXISTENCE; REGULARITY; SPHERES; FOLIATION;
D O I：
10.1007/s00222-019-00886-1
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
引用
收藏
页码：441 / 490
页数：50
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