Seminars & Colloquia Calendar
Generic Regularity for All Minimal Hypersurfaces in 8-Manifolds
Zhihan Wang (Princeton University)
Date & time: Tuesday, 25 October 2022 at 2:50PM - 3:50PM
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.