Minimal hypersurfaces with bounded index

• 成果类型: Article
• 署名作者: Chodosh, Otis; Ketover, Daniel; Maximo, Davi
• 署名单位: University of Cambridge; Princeton University; Stanford University; University of Pennsylvania
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-017-0717-5
• 发表日期: 2017
• 页码: 617-664
• 关键词: morse index; SURFACES; CURVATURE; EXISTENCE; REGULARITY; AREA; 3-manifolds; laminations; compactness; uniqueness

摘要

We prove a structural theorem that provides a precise local picture of how a sequence of closed embedded minimal hypersurfaces with uniformly bounded index (and volume if the ambient dimension is greater than three) in a Riemannian manifold (M-n, g), 3 <= n <= 7 can degenerate. Loosely speaking, our results show that embedded minimal hypersurfaces with bounded index behave qualitatively like embedded stable minimal hypersurfaces, up to controlled errors. Several compactness/finiteness theorems follow from our local picture.