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The Stability of Self-Shrinkers of Mean Curvature Flow in Higher Codimension

In this paper, we generalize Colding and Minicozzi's work \cite{CM} on the stability of self-shrinkers in the hypersurface case to higher co-dimensional cases. The first and second variation formulae of the $F$-functional are derived and an equivalent condition to the stability in general codimension is found. Moreover, we show that the closed Lagrangian self-shrinkers given by Anciaux in \cite{An} are unstable.

preprint2012arXivOpen access
Yng-Ing LeeYang-Kai Lue
math.DG
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Yng-Ing LeeYang-Kai Lue

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