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Asymptotic structure of almost eigenfunctions of drift Laplacians on conical ends
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 142, Number 6, December 2020
- pp. 1897-1929
- 10.1353/ajm.2020.0047
- Article
- Additional Information
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Abstract
Abstract:
We use a weighted variant of the frequency functions introduced by Almgren to prove sharp asymptotic estimates for almost eigenfunctions of the drift Laplacian associated to the Gaussian weight on an asymptotically conical end. As a consequence, we obtain a purely elliptic proof of a result of L. Wang on the uniqueness of self-shrinkers of the mean curvature flow asymptotic to a given cone. Another consequence is a unique continuation property for self-expanders of the mean curvature flow that flow from a cone.
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