學術報告

【online】 Ancient finite entropy flows by powers of curvature in R^2

發布人：發布時間： 2020-12-14

字體大小： 【小】 【中】 【大】

**題目: **Ancient finite entropy flows by powers of curvature in R^2

**報告人：**孫黎明 （The University of British Columbia）

**時間：**2020年12月25日 10:00-12:00

**地點：**zoom會議室 **ID：**680 4084 2281 **PW：**595265

**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 are 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. This work is joint with Keysongsu Choi.

**邀請人：**陳學長 老師