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September 2013 Volume growth eigenvalue and compactness for self-shrinkers
Qi Ding, Y. L. Xin
Asian J. Math. 17(3): 443-456 (September 2013).

Abstract

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 Yau. By the eigenvalue estimates, we can prove a compactness theorem on a class of compact self-shrinkers in $\mathbb{R}^3$ obtained by Colding-Minicozzi under weaker conditions.

Citation

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Qi Ding. Y. L. Xin. "Volume growth eigenvalue and compactness for self-shrinkers." Asian J. Math. 17 (3) 443 - 456, September 2013.

Information

Published: September 2013
First available in Project Euclid: 8 November 2013

zbMATH: 1283.53062
MathSciNet: MR3119795

Subjects:
Primary: 53A07, 53A10, 53C21, 53C44

Rights: Copyright © 2013 International Press of Boston

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Vol.17 • No. 3 • September 2013
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