## 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.## References

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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
- Received by editor(s): July 18, 2012
- Published electronically: November 24, 2014
- © Copyright 2014
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 3301868