The stability of self-shrinkers of mean curvature flow in higher co-dimension

Lee, Yng-Ing; Lue, Yang-Kai

doi:10.1090/S0002-9947-2014-05969-2

The stability of self-shrinkers of mean curvature flow in higher co-dimension
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by Yng-Ing Lee and Yang-Kai Lue PDF

Trans. Amer. Math. Soc. 367 (2015), 2411-2435 Request permission

Abstract:

We generalize Colding and Minicozzi’s work (2012) on the stability of hypersurface self-shrinkers to higher co-dimension. The first and second variation formulae of the $F$-functional are derived and an equivalent condition to the stability in general co-dimension is found. We also prove that $\mathbb R^n$ is the only stable product self-shrinker and show that the closed embedded Lagrangian self-shrinkers constructed by Anciaux are unstable.

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