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math.DG2025
Local mollification of metrics with small curvature concentration
Man-Chun Lee, Tang-Kai Lee
In this work, we establish a local smoothing result on metrics with small curvature concentration with respect to Sobolev constants and volume growth. In contrast with all previous…
math.DG2025
An Intersection Principle for Mean Curvature Flow
Tang-Kai Lee, Alec Payne
The avoidance principle says that mean curvature flows of hypersurfaces remain disjoint if they are disjoint at the initial time. We prove several generalizations of the avoidance…
math.DG2025
Planarity and convexity for pinched ancient solutions of mean curvature flow
Tang-Kai Lee, Keaton Naff, Jingze Zhu
We prove a parabolically scale-invariant variation of the planarity estimate in \cite{Na22} for higher codimension mean curvature flow, borrowing ideas from work of Brendle--Huiske…