## Uniqueness of self-similar shrinkers with asymptotically conical ends

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- by Lu Wang
- J. Amer. Math. Soc.
**27**(2014), 613-638 - DOI: https://doi.org/10.1090/S0894-0347-2014-00792-X
- Published electronically: March 19, 2014
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## Abstract:

Let $C\subset \mathbb {R}^{n+1}$ be a regular cone with vertex at the origin. In this paper, we show the uniqueness for smooth properly embedded self-shrinking ends in $\mathbb {R}^{n+1}$ that are asymptotic to $C$. As an application, we prove that not every regular cone with vertex at the origin has a smooth complete properly embedded self-shrinker asymptotic to it.## References

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## Bibliographic Information

**Lu Wang**- Affiliation:
Department of Mathematics, Johns Hopkins University, 3400 N. Charles Street, Baltimore

, Maryland 21218

- Email: coral0426@gmail.com
- Received by editor(s): October 3, 2011
- Received by editor(s) in revised form: June 27, 2013, and October 19, 2013
- Published electronically: March 19, 2014
- © Copyright 2014 American Mathematical Society
- Journal: J. Amer. Math. Soc.
**27**(2014), 613-638 - MSC (2010): Primary 53C44, 53C24, 35J15; Secondary 35B60
- DOI: https://doi.org/10.1090/S0894-0347-2014-00792-X
- MathSciNet review: 3194490