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arXiv · 1306.1398

Curve shortening-straightening flow for non-closed planar curves with infinite length

Matteo Novaga·Shinya Okabe
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Abstract

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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Matteo Novaga, Shinya Okabe. 2013-06-06. Curve shortening-straightening flow for non-closed planar curves with infinite length. https://arxiv.org/abs/1306.1398

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