Year: 2025
Type: article
Abstract: We show that in an 8-dimensional closed Riemmanian manifold with $C^{\infty }$ C ∞ -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.
Source: Inventiones mathematicae
Authors: Yangyang Li, Zhihan Wang
Institution: University of Chicago
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
OpenAlex ID: W4409187975