Volume growth, eigenvalue and compactness for self-shrinkers

Details Volume growth, eigenvalue and compactness for self-shrinkers Volume growth, eigenvalue and compactness for self-shrinkers

2011-01-07

arxiv.org/abs/1101.1411v1

Mathematics

Differential Geometry

22 pages

Scientific paper

In this paper, we show an optimal volume growth for self-shrinkers, and
estimate a lower bound of the first eigenvalue of $\mathcal{L}$ operator on
self-shrinkers, inspired by the first eigenvalue conjecture on minimal
hypersurfaces in the unit sphere. By the eigenvalue estimates, we can prove a
compactness theorem obtained by Colding-Minicozzi under weaker conditions.

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