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arXiv · 2012.10022

The length-constrained ideal curve flow

James McCoy·Glen Wheeler·Yuhan Wu
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Abstract

A recent article by the first two authors together with B Andrews and V-M Wheeler 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 $L^2$ sense. Critical in the analysis 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.

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James McCoy, Glen Wheeler, Yuhan Wu. 2020-12-18. The length-constrained ideal curve flow. https://arxiv.org/abs/2012.10022

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