Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	王志涵，Princeton University
Inviter:	孙黎明
Title:	Generic Regularity for All Minimal Hypersurfaces in 8-Manifolds
Language:	Chinese
Time & Venue:	2022.12.01 09:00-10:00 腾讯会议: 827-698-748 密码：123456
Abstract:	The well-known Simons cone suggests that singularities may exist in a stable minimal hypersurface in Riemannian manifolds of dimension greater than 7, locally modeled on stable minimal hypercones. It was conjectured that generically they can be perturbed away. In this talk, we present a way to eliminate these singularities by perturbing metric in an 8-manifold. By combining with a Sard-Type Theorem for space of singular minimal hypersurfaces of dimension 7, joint with Yangyang Li, we proved that in an 8-manifold with generic metric, every locally stable minimal hypersurface has no singularity. In particular, this proves the existence of infinitely many SMOOTH minimal hypersurfaces in a generic 8-manifold.