$\mathcal{F}$-stability for self-shrinking solutions to mean curvature flow

Details $\mathcal{F}$-stability for self-shrinking solutions to mean curvature flow $\mathcal{F}$-stability for self-shrinking solutions to mean curvature flow

2012-04-23

arxiv.org/abs/1204.5010v1

Mathematics

Differential Geometry

23 pages

Scientific paper

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, in codimension one case, our results reduce to
Colding-Minicozzi's results.

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