非线性分析研讨班：Generic Regularity for All Minimal Hypersurfaces in 8-Manifolds

中科院数学与系统科学研究院

数学研究所

学术报告

非线性分析研讨班

报告人：王志涵 (Princeton University)

题  目：Generic Regularity for All Minimal Hypersurfaces in 8-Manifolds

时  间：2022.12.01（星期四）上午09:00-10:00

地  点：腾讯会议: 827-698-748 密码：123456

摘  要：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.