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arXiv · 1603.06539

The index of shrinkers of the mean curvature flow

Zihan Hans Liu
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Abstract

We introduce a notion of index for shrinkers of the mean curvature flow. We then prove a gap theorem for the index of rotationally symmetric immersed shrinkers in R^3, namely, that such shrinkers have index at least 3, unless they are one of the stable ones: the sphere, the cylinder, or the plane. We also provide a generalization of the result to higher dimensions.

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Zihan Hans Liu. 2016-03-21. The index of shrinkers of the mean curvature flow. https://arxiv.org/abs/1603.06539

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