Geometric Analysis and Topology Seminar

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Generic Regularity for All Minimal Hypersurfaces in 8-Manifolds

Speaker: Zhihan Wang, Princeton University

Location: Online

Videoconference link: https://nyu.zoom.us/j/94747124588

Date: Wednesday, February 23, 2022, 11 a.m.

Synopsis:

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, we proves 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.