【Title】 Uniqueness of the Ecker-Huisken flow under some asymptotic assumption
【Abstract】When discussing the uniqueness of geometric flow, it's important to declare the uniqueness in which class. For the Ecker-Huisken flow, the one-dimensional graphical curve shortening flow, the uniqueness is known when the solution converges to the initial data in the sense of either with or , which was developed by [Chou-Kwong, 2020] and [Daskalopoulos-Saez, 2023], respectively. In this talk, I will present a recent result on the uniqueness of the Ecker-Huisken flow for some specific decayed initial data. The contribution in this result is we only assume the -convergence to the initial data for some compact subset . This is a joint work with Prof. Peter Topping during this research abroad.
報告人二 : 許嘉麟(NTU) 16:30~17:30
【Title】 Deformation of Symplectic Surfaces in Under the Mean Curvature Flow
【Abstract】Constructing singularities of higher-codimension mean curvature flow has recently been paid significant attention to. In the early development of geometric measure theory, Federer investigated complex projective varieties as the first examples of minimal currents with interesting singularities.This sparked the study of various stability of submanifolds, including the dynamical stability of simple normal crossing algebraic curves in under the mean curvature flow. In this talk, I will discuss these historical developments and my ongoing research project on constructing the mean curvature flow of branched surfaces deforming into a cuspidal curve in .
