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Proceedings of the American Mathematical Society

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The mean curvature flow by parallel hypersurfaces


Authors: Hiuri Fellipe Santos dos Reis and Keti Tenenblat
Journal: Proc. Amer. Math. Soc. 146 (2018), 4867-4878
MSC (2010): Primary 53C44
DOI: https://doi.org/10.1090/proc/14178
Published electronically: July 23, 2018
MathSciNet review: 3856153
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Abstract: It is shown that a hypersurface of a space form is the initial data for a solution to the mean curvature flow by parallel hypersurfaces if and only if it is isoparametric. By solving an ordinary differential equation, explicit solutions are given for all isoparametric hypersurfaces of space forms. In particular, for such hypersurfaces of the sphere, the exact collapsing time into a focal submanifold is given in terms of its dimension, the principal curvatures, and their multiplicities.


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Additional Information

Hiuri Fellipe Santos dos Reis
Affiliation: Department of Mathematics, Universidade de Brasília, 70910-900, Brasília-DF, Brazil
Email: hiuri.reis@ifg.edu.br

Keti Tenenblat
Affiliation: Department of Mathematics, Universidade de Brasília, 70910-900, Brasília-DF, Brazil
Email: K.Tenenblat@mat.unb.br

DOI: https://doi.org/10.1090/proc/14178
Keywords: Isoparametric hypersurface, mean curvature flow, parallel hypersurface, space forms
Received by editor(s): October 2, 2017
Published electronically: July 23, 2018
Additional Notes: The first author was partially supported by CNPq Proc. 141275/2014-6, Ministry of Science and Technology, Brazil
The second author was partially supported by CNPq Proc. 312462/2014-0, Ministry of Science and Technology, Brazil
Communicated by: Lei Ni
Article copyright: © Copyright 2018 American Mathematical Society