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November 2014 $\mathcal{F}$-stability for self-shrinking solutions to mean curvature flow
Ben Andrews, Haizhong Li, Yong Wei
Asian J. Math. 18(5): 757-778 (November 2014).

Abstract

In this paper, we formulate the notion of the $\mathcal{F}$-stability of self-shrinking solutions to mean curvature flow in arbitrary codimension. Then we give some classifications of the $\mathcal{F}$-stable self-shrinkers in arbitrary codimension. We show that the only $\mathcal{F}$-stable self-shrinking solution which is a closed minimal submanifold in a sphere must be the shrinking sphere. We also prove that the spheres and planes are the only $\mathcal{F}$-stable self-shrinkers with parallel principal normal. In the codimension one case, our results reduce to those of Colding and Minicozzi.

Citation

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Ben Andrews. Haizhong Li. Yong Wei. "$\mathcal{F}$-stability for self-shrinking solutions to mean curvature flow." Asian J. Math. 18 (5) 757 - 778, November 2014.

Information

Published: November 2014
First available in Project Euclid: 2 December 2014

zbMATH: 1306.53059
MathSciNet: MR3287002

Subjects:
Primary: 53C44
Secondary: 53C42

Rights: Copyright © 2014 International Press of Boston

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Vol.18 • No. 5 • November 2014
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