A Length-Constrained Ideal Curve Flow

Title: A Length-Constrained Ideal Curve Flow
Creator: McCoy, James A.; Wheeler, Glen E.; Wu, Yuhan
Relation: ARC.DP180100431 http://purl.org/au-research/grants/arc/DP180100431
Relation: Quarterly Journal of Mathematics Vol. 73, Issue 2, p. 685-699
Publisher Link: http://dx.doi.org/10.1093/qmath/haab050
Publisher: Oxford University Press
Resource Type: journal article
Date: 2022
Description: A recent article [1] considered the so-called ‘ideal curve flow’, a sixth-order curvature flow that seeks to deform closed planar curves to curves with least variation of total geodesic curvature in the L2 sense. It was critical in the analysis in that article that there was a length bound on the evolving curves. It is natural to suspect therefore that the length-constrained ideal curve flow should permit a more straightforward analysis, at least in the case of small initial ‘energy’. In this article we show this is indeed the case, with suitable initial data providing a flow that exists for all time and converges smoothly and exponentially to a multiply-covered round circle of the same length and winding number as the initial curve.
Subject: curvature; curve flow; planar curves; geodesic curvature
Identifier: http://hdl.handle.net/1959.13/1464663
Identifier: uon:47068
Identifier: ISSN:0033-5606
Language: eng
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