Minimal hypersurfaces for generic metrics in dimension 8

• 成果类型: Article
• 署名作者: Li, Yangyang; Wang, Zhihan
• 署名单位: University of Chicago
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-025-01333-0
• 发表日期: 2025
• 页码: 1193-1303
• 关键词: strong maximum principle; HARMONIC MAPS; EXISTENCE; REGULARITY; AREA; multiplicity; MANIFOLDS; SURFACES; THEOREM; SPACE

摘要

We show that in an 8-dimensional closed Riemmanian manifold with Cam-generic metrics, every minimal hypersurface is smooth and nondegenerate. This confirms a full generic regularity conjecture of minimal hypersurfaces in dimension eight. This also enables us to generalize many generic geometric properties of (Almgren-Pitts) min-max minimal hypersurfaces, previously only known in low dimensions, to dimension eight. En route to our main results, we have proved a sheeting theorem for minimal hypersurfaces in dimension 8 (Appendix C), which gives an affirmed answer to a question asked by Ilmanen in dimension 8.