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


Authors: Yng-Ing Lee and Yang-Kai Lue
Journal: Trans. Amer. Math. Soc. 367 (2015), 2411-2435
MSC (2010): Primary 53C44, 35C06
DOI: https://doi.org/10.1090/S0002-9947-2014-05969-2
Published electronically: November 24, 2014
MathSciNet review: 3301868
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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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Additional Information

Yng-Ing Lee
Affiliation: Department of Mathematics, National Taiwan University, Taipei, Taiwan – and – National Center for Theoretical Sciences, Taipei Office, Taipei, Taiwan
Email: yilee@math.ntu.edu.tw

Yang-Kai Lue
Affiliation: Department of Mathematics, National Taiwan University, Taipei, Taiwan
Address at time of publication: Department of Mathematics, National Taiwan Normal University, Hsinchu, Taiwan
Email: luf961@yahoo.com.tw

DOI: https://doi.org/10.1090/S0002-9947-2014-05969-2
Received by editor(s): July 18, 2012
Published electronically: November 24, 2014
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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