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The length-constrained ideal curve flow

Journal Article


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.

Publication Date


  • 2020

Citation


  • McCoy, J., Wheeler, G., & Wu, Y. (2020). The length-constrained ideal curve flow. Retrieved from http://arxiv.org/abs/2012.10022v1

Web Of Science Accession Number


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.

Publication Date


  • 2020

Citation


  • McCoy, J., Wheeler, G., & Wu, Y. (2020). The length-constrained ideal curve flow. Retrieved from http://arxiv.org/abs/2012.10022v1

Web Of Science Accession Number