Yng-Ing Lee, Yang-Kai Lue
Published 2012-04-27Version 1
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.
Comments: We in the end of 2010, obtained the same foundation part of the article arXiv:1204.5010v1 by B. Andrews, H. Li and Y. Wei, entitled with "F-stability for self-shrinking solutions to mean curvature flow". In our article, we at the same time showed the unstability of Anciaux's closed Lagrangian self-shrinkers
Mean curvature flow in higher codimension
The extension and convergence of mean curvature flow in higher codimension
Mean curvature flow of higher codimension in Riemannian manifolds
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