Existence of infinitely many minimal hypersurfaces in closed manifolds

• 成果类型: Article
• 署名作者: Song, Antoine
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2023.197.3.1
• 发表日期: 2023
• 页码: 859-895
• 关键词: min-max theory; MAXIMUM PRINCIPLE; multiplicity; REGULARITY; RIGIDITY

摘要

Using min-max theory, we show that in any closed Riemannian manifold of dimension at least 3 and at most 7, there exist infinitely many smoothly embedded closed minimal hypersurfaces. It proves a conjecture of S.-T. Yau. This paper builds on the methods developed by F. C. Marques and A. Neves.