The mean curvature flow by parallel hypersurfaces

dos Reis, Hiuri; Tenenblat, Keti

doi:10.1090/proc/14178

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.

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