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math.AP2024
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…
math.DG2024
Arnold-Thom conjecture for the arrival time of surfaces
Tang-Kai Lee, Jingze Zhu
Following Łojasiewicz's uniqueness theorem and Thom's gradient conjecture, Arnold proposed a stronger version about the existence of limit tangents of gradient flow lines for analy…