Min-max theory for constant mean curvature hypersurfaces

• 成果类型: Article
• 署名作者: Zhou, Xin; Zhu, Jonathan J.
• 署名单位: University of California System; University of California Santa Barbara; Harvard University; Princeton University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-019-00886-1
• 发表日期: 2019
• 页码: 441-490
• 关键词: minimal hypersurfaces; SURFACES; EXISTENCE; REGULARITY; spheres; foliation

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.