中科院数学与系统科学研究院
数学研究所
偏微分方程研讨班
报告人： 孙黎明 博士 (University of British Columbia)
题 目：Ancient finite entropy flows by powers of curvature in R2
时 间：2020.12.07（星期一）, 10:30-11:30
地 点：数学院南楼N202
Zoom会议：696 4350 7378 密码：527979
摘 要：Ancient flows have been intensively studied in the mean curvature flow, a higher dimensional version of the curve-shortening flow. In particular, ancient mean curvature flows are useful to investigate singularities. In this talk, I will be talking about our study of the ancient solution of alpha-curve-shortening flow in R^2. Daskalopoulos, Hamilton, and Sesum classify ancient solutions for alpha=1 case, however, for alpha<1, very few is known and especially for small ones. Along this direction, we first construct a family of non-homothetic ancient flows whose entropy is finite. We determine the Morse indices and kernels of the linearized operator of self-shrinkers to the flows. Conversely, we are able to classify all the ancient solutions with finite entropy. It turns out all ancient solutions have the same asymptotic as the ones we have constructed.
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