The mean curvature flow for isoparametric submanifolds

Details The mean curvature flow for isoparametric submanifolds The mean curvature flow for isoparametric submanifolds

2007-06-25

arxiv.org/abs/0706.3550v1

Mathematics

Differential Geometry

25 pages, LaTex format

Scientific paper

A submanifold in space forms is isoparametric if the normal bundle is flat and principal curvatures along any parallel normal fields are constant. We study the mean curvature flow with initial data an isoparametric submanifold in Euclidean space and sphere. We show that the mean curvature flow preserves the isoparametric condition, develops singularities in finite time, and converges in finite time to a smooth submanifold of lower dimension. We also give a precise description of the collapsing.

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