论文标题
单调凸功能产生的旋转表面上的曲线缩短流量
Curve shortening flows on rotational surfaces generated by monotone convex functions
论文作者
论文摘要
在本文中，我们研究了$ \ mathbb {r}^3 $的旋转表面上的曲线缩短流。我们假设表面具有负高斯曲率，并且某些条件与高斯曲率和嵌入式曲线的曲率有关。在这些假设下，我们证明曲线在沿流动的旋转表面的相似之处上保持图。此外，我们证明了比较原理和流动的长期存在。
In this paper, we study curve shortening flows on rotational surfaces in $\mathbb{R}^3$. We assume that the surfaces have negative Gauss curvatures and that some condition related to the Gauss curvature and the curvature of embedded curve holds on them. Under these assumptions, we prove that the curve remains a graph over the parallels of the rotational surface along the flow. Also, we prove the comparison principle and the long-time existence of the flow.
