论文标题
具有有限的总曲率翻译表面的结构
The Structure of Translating Surfaces with Finite Total Curvature
论文作者
论文摘要
在本文中，我们证明任何平均曲率流动转换器$σ^2 \ subset \ mathbb {r}^3 $具有有限的总曲率，一端必须是平面。我们还证明，如果翻译器$σ$具有多个目的，则它们是包含翻译方向的平面$π$渐近，并且可以写成$π$的图形。最后，我们确定$σ$的末端对$π$是渐近的，并获得了其渐近行为的定量估计。
In this paper, we prove that any mean curvature flow translator $Σ^2 \subset \mathbb{R}^3$ with finite total curvature and one end must be a plane. We also prove that if the translator $Σ$ has multiple ends, they are asymptotic to a plane $Π$ containing the direction of translation and can be written as graphs over $Π$. Finally, we determine that the ends of $Σ$ are strongly asymptotic to $Π$ and obtain quantitative estimates for their asymptotic behavior.
