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.

中文翻译：

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锥形末端上漂移拉普拉斯算子的本征函数的渐近结构

摘要：

我们使用Almgren引入的频率函数的加权变体来证明与渐近圆锥形端上的高斯权重相关的漂移拉普拉斯算子的几乎本征函数的清晰渐近估计。结果，我们获得了L. Wang关于给定圆锥渐近平均曲率流的自收缩的唯一性的纯椭圆证明。另一个结果是从圆锥体流出的平均曲率流的自扩张器具有独特的连续性。