Asymptotic structure of almost eigenfunctions of drift Laplacians on conical ends

2017/08/23 by Jacob Bernstein, Bernstein, Jacob · 1 citation
Mathematics · #35J15 #53C44 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #math.AP #math.DG #msc:35J15 #msc:53C44

paper · pdf · doi:10.48550/arxiv.1708.07085

26 pages. Fixed typos and included additional references. Weakened hypotheses of Theorem 9.1

arxiv created 2017/12/13 · arxiv updated 2017/12/14

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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