The mean curvature flow by parallel hypersurfaces
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- by Hiuri Fellipe Santos dos Reis and Keti Tenenblat PDF
- Proc. Amer. Math. Soc. 146 (2018), 4867-4878 Request permission
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.References
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Additional Information
- Hiuri Fellipe Santos dos Reis
- Affiliation: Department of Mathematics, Universidade de Brasília, 70910-900, Brasília-DF, Brazil
- MR Author ID: 1287830
- Email: hiuri.reis@ifg.edu.br
- Keti Tenenblat
- Affiliation: Department of Mathematics, Universidade de Brasília, 70910-900, Brasília-DF, Brazil
- MR Author ID: 171535
- Email: K.Tenenblat@mat.unb.br
- 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
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 4867-4878
- MSC (2010): Primary 53C44
- DOI: https://doi.org/10.1090/proc/14178
- MathSciNet review: 3856153