无限长非封闭平面曲线的曲线缩短-矫直流程
Curve shortening-straightening flow for non-closed planar curves with infinite length
摘要：
考虑无限长非闭平面曲线的运动。该运动由几何泛函的最速下降流控制，该几何泛函由长度泛函和总平方曲率之和组成。我们把这种流动称为缩短-矫直流动。本文首先证明了无限长非闭平面曲线的缩短-矫直流的一个长时间存在性结果。然后，我们证明了解决方案收敛到一个固定的解决方案，随着时间的推移到无穷大。此外，我们还给出了定态解的分类。
英文摘要：
We consider a motion of non-closed planar curves with infinite length. The motion is governed by a steepest descent flow for the geometric functional which consists of the sum of the length functional and the total squared curvature. We call the flow shortening-straightening flow. In this paper, first we prove a long time existence result for the shortening-straightening flow for non-closed planar curves with infinite length. Then we show that the solution converges to a stationary solution as time goes to infinity. Moreover we give a classification of the stationary solution.
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