We show that two properly embedded self-shrinkers in Euclidean space that are sufficiently separated at infinity must intersect at a finite point. The proof is based on a localized version of the Reilly formula applied to a suitable f -harmonic function with controlled gradient. In the immersed case, a new direct proof of the generalized half-space property is also presented.

中文翻译：

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从椭圆形偏微分方程的角度来看，自收缩器具有Frankel性质

我们表明，在欧几里得空间中两个充分嵌入的自收缩子在无限远处必须充分分离，它们必须在一个有限点处相交。该证明基于赖利公式的本地化版本，该版本适用于具有受控梯度的合适f调和函数。在沉浸的情况下，还提出了广义半空间性质的新直接证明。