Abstract

A central problem in differential geometry is understanding how the geometry of a boundary determines the geometry of its interior. Gromov's fill-in problem suggests that when a closed Riemannian manifold is filled with a region of large curvature, the extrinsic curvature of the boundary must be bounded above in some sense. The fill-in problem, particularly in the context of scalar curvature, is closely related to certain notions of quasi-local mass in general relativity. In this talk, I will discuss some recent progress on the scalar curvature fill-in problem under the hyperbolic setting.

Biography

I am a 4th-year Ph.D. student at Columbia University, under the guidance of Professor Simon Brendle. My research interests lie in geometric analysis and various aspects of differential geometry. Currently, I am focused on investigating problems related to minimal surfaces and the geometry of manifolds with positive scalar curvature.

Zoom meeting

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