Room 202, Astronomy-Mathematics Building, NTU

(台灣大學天文數學館 202室)

The Stability of Self-shrinkers of Mean Curvature Flow

Yang-Kai Lue (NCTS)

Abstract

From Huisken's monotonicity formula, self-shrinkers describe all possible central blow-up limits of a finite-time singularity of mean curvature flow. We introduce the $F$-functional. Self-shrinkers are critical points of the $F$-functional. Using the second variation of the $F$-functional, some self-shrinkers can be classified. I will talk about recent classification results of self-shrinkers.