数学研究所

中国科学院华罗庚数学重点实验室

华罗庚青年数学论坛综合报告

报告人：王志涵（康奈尔大学）

题 目：Generic Regularity of Minimal Submanifolds with Isolated Singularities

时  间：2024.12.24（星期二）10:30-11:30

地  点：晨兴110

摘  要：Singularities are commonly found in geometric variational objects, such as minimal submanifolds, where they are locally modeled on minimal cones. Despite the abundance of singularity models constructed in the literature, it is conjectured that in generic settings, they are significantly simpler.

In this talk, we present a characterization of minimal cones that can serve as singularity models for minimal submanifolds with isolated singularities in a generic Riemannian manifold, without imposing additional constraint on dimension or codimension. As an application, we shall discuss a generic finiteness result of low area minimal hypersurfaces in nearly round 4-spheres. This is based on the joint work with Alessandro Carlotto and Yangyang Li.