Existence of minimal hypersurfaces in complete manifolds of finite volume

• 成果类型: Article
• 署名作者: Chambers, Gregory R.; Liokumovich, Yevgeny
• 署名单位: Rice University; Massachusetts Institute of Technology (MIT); University of Toronto
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-019-00903-3
• 发表日期: 2020
• 页码: 179-217
• 关键词: closed geodesics; width

摘要

We prove that every complete non-compact manifold of finite volume contains a (possibly non-compact) minimal hypersurface of finite volume. The main tool is the following result of independent interest: if a region U can be swept out by a family of hypersurfaces of volume at most V, then it can be swept out by a family of mutually disjoint hypersurfaces of volume at most V+epsilon.