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Geometric Analysis Seminar

Dynamics of Singularities of Mean Curvature Flow

Ao Sun - University of Chicago

Location:  Zoom
Date & time: Tuesday, 12 April 2022 at 2:50PM - 3:50PM

Abstract: As a nonlinear geometric heat flow, mean curvature flow has complicated singularity structures. We prove that, nevertheless, starting from a generic set of hypersurfaces, the mean curvature flow has simpler singularity structures. Our results include how to perturb the initial data to avoid complicated singularities, and how to perturb the initial data to obtain a specific pattern of the singularities. Among the applications, we prove that generically the arrival time formulation of level set flow has low regularity. The key of our results is to study the singularities from a global dynamic view. This talk is based on my joint work with Jinxin Xue (Tsinghua University).

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