Calculus of Variations and Geometric Measure Theory
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M. Novaga - S. Okabe

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

created by novaga on 25 Oct 2012
modified on 02 Jan 2018

[BibTeX]

Published Paper

Inserted: 25 oct 2012
Last Updated: 2 jan 2018

Journal: J. Differential Eqs.
Volume: 256
Number: 3
Pages: 1093-1132
Year: 2014

ArXiv: 1306.1398 PDF

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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