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.