6 papers
Non-uniqueness of geodesic limits and a question of Grayson and Gage
Shrey Aryan, Tang-Kai Lee
Grayson and Gage proved that an immortal curve shortening flow of simple closed curves on a closed surface converges subsequentially to a closed geodesic, and they asked whether th…
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…
Arnold-Thom conjecture for the arrival time of surfaces
Tang-Kai Lee, Jingze Zhu
Following Åojasiewicz's uniqueness theorem and Thom's gradient conjecture, Arnold proposed a stronger version about the existence of limit tangents of gradient flow lines for anal…
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…
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…
Ancient caloric functions and parabolic frequency on graphs
Tang-Kai Lee, Archana Mohandas
We study ancient solutions to discrete heat equations on some weighted graphs. On a graph of the form of a product with $\bb Z,$ we show that there are no non-trivial ancient solut…