论文标题
用于一般旋转数的平面曲线的非本地曲率流的渐近分析
Asymptotic analysis for non-local curvature flows for plane curves with a general rotation number
论文作者
论文摘要
在这项工作中讨论了几个具有一般旋转数的平面曲线的非本地曲率流。流的类型包括保护区域的流量和长度保护流。对于旋转第一的平面曲线，我们对这些流动的这些流有相对较好的理解。特别是，当初始曲线严格凸出时，流动在全球存在，并且随着时间倾向于无穷大。即使初始曲线不是严格凸出的，如果存在的全局解决方案也会收敛到圆。在这里，我们处理具有一般旋转数量的曲线，并且不仅显示了全球解决方案的相似结果，而且还显示出爆炸标准，爆炸时间的上限估计以及下方的爆破速率。为此，我们使用以前从未考虑过的几何数量。
Several non-local curvature flows for plane curves with a general rotation number are discussed in this work. The types of flows include the area-preserving flow and the length-preserving flow. We have a relatively good understanding of these flows for plane curves with the rotation number one. In particular, when the initial curve is strictly convex, the flow exists globally in time, and converges to a circle as time tends to infinity. Even if the initial curve is not strictly convex, a global solution, if it exists, converges to a circle. Here, we deal with curves with a general rotation number, and show, not only a similar result for global solutions, but also a blow-up criterion, upper estimates of the blow-up time, and blow-up rate from below. For this purpose, we use a geometric quantity which has never been considered before.
