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 F -functional are derived and an equivalent condition to the stability in general co-dimension is found. We also prove that R n \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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