臺灣大學: 數學研究所李瑩英呂楊凱Lue, Yang-KaiYang-KaiLue2013-03-212018-06-282013-03-212018-06-282012http://ntur.lib.ntu.edu.tw//handle/246246/249921In 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.432448 bytesapplication/pdfen-US拉格拉奇同構解均曲率Self-Similar solutionLagrangianmean curvature vectorthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/249921/1/ntu-101-D95221005-1.pdf