Density of minimal hypersurfaces for generic metrics

• 成果类型: Article
• 署名作者: Irie, Kei; Marques, Fernando C.; Neves, Andre
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2018.187.3.8
• 发表日期: 2018
• 页码: 963-972
• 关键词: Existence; submanifolds; index; SPACE

摘要

For almost all Riemannian metrics (in the C-infinity Baire sense) on a closed manifold Mn+1, 3 <= (n + 1) <= 7, we prove that the union of all closed, smooth, embedded minimal hypersurfaces is dense. This implies there are infinitely many minimal hypersurfaces, thus proving a conjecture of Yau (1982) for generic metrics.