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arXiv · 1204.6116

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

Yng-Ing Lee·Yang-Kai Lue
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Abstract

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.

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Yng-Ing Lee, Yang-Kai Lue. 2012-04-27. The Stability of Self-Shrinkers of Mean Curvature Flow in Higher Codimension. https://arxiv.org/abs/1204.6116

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