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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圆锥端漂移拉普拉斯算子的近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锐渐近估计。因此，我们获得了 L. Wang 关于渐近给定锥的平均曲率流的自收缩的唯一性的结果的纯椭圆证明。另一个结果是从锥体流出的平均曲率流的自膨胀器具有独特的连续性。