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15 March 2009 The mean curvature flow for isoparametric submanifolds
Xiaobo Liu, Chuu-Lian Terng
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Duke Math. J. 147(1): 157-179 (15 March 2009). DOI: 10.1215/00127094-2009-009

Abstract

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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Xiaobo Liu. Chuu-Lian Terng. "The mean curvature flow for isoparametric submanifolds." Duke Math. J. 147 (1) 157 - 179, 15 March 2009. https://doi.org/10.1215/00127094-2009-009

Information

Published: 15 March 2009
First available in Project Euclid: 26 February 2009

zbMATH: 1172.53044
MathSciNet: MR2494459
Digital Object Identifier: 10.1215/00127094-2009-009

Subjects:
Primary: 53C21
Secondary: 58J35

Rights: Copyright © 2009 Duke University Press

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Vol.147 • No. 1 • 15 March 2009
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