均曲率流的拉格拉奇自同構解

Abstract

In this thesis, we generalize Colding and Minicozzi's work on the stability of self-shrinkers in the hypersurface case to higher co-dimensional cases. The 1st and 2nd variation formulae of the $F$-functional are derived and an equivalent condition to the stability in general codimension is found. Using the equivalent condition, we can classify $F$-stable product self-shrinkers and show that the Lagrangian self-shrinkers given by Anciaux are $F$- unstable.