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Self-shrinkers to the mean curvature flow asymptotic to isoparametric cones


Authors: Po-Yao Chang and Joel Spruck
Journal: Trans. Amer. Math. Soc. 369 (2017), 6565-6582
MSC (2010): Primary 53C44, 53C40
DOI: https://doi.org/10.1090/tran/6957
Published electronically: May 5, 2017
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Abstract: In this paper we construct an end of a self-similar shrinking solution of the mean curvature flow asymptotic to an isoparametric cone $ C$ and lying outside $ C$. We call a cone $ C$ in $ \mathbb{R}^{n+1}$ an isoparametric cone if $ C$ is the cone over a compact embedded isoparametric hypersurface $ \Gamma \subset \mathbb{S}^n$. The theory of isoparametic hypersurfaces is extremely rich, and there are infinitely many distinct classes of examples, each with infinitely many members.


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Additional Information

Po-Yao Chang
Affiliation: Department of Mathematics, Johns Hopkins University, Baltimore, Maryland 21218
Email: poyaostevenchang@gmail.com

Joel Spruck
Affiliation: Department of Mathematics, Johns Hopkins University, Baltimore, Maryland 21218
Email: js@math.jhu.edu

DOI: https://doi.org/10.1090/tran/6957
Keywords: Self-shrinker, isoparametric
Received by editor(s): October 24, 2015
Received by editor(s) in revised form: April 17, 2016
Published electronically: May 5, 2017
Additional Notes: The authors’ research was supported in part by the NSF
Article copyright: © Copyright 2017 American Mathematical Society

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