论文标题
长度约束的理想曲线流
The length-constrained ideal curve flow
论文作者
论文摘要
前两位作者最近的一篇文章与B Andrews和V-M Wheeler一起考虑了所谓的“理想曲线流”，这是第六阶曲率流，旨在将封闭的平面曲线变形，以在$ l^2 $的情况下变形，总测量曲率变化最小。在分析中至关重要的是，在不断发展的曲线上有一个长度结合。因此，很自然地怀疑，至少在初始“能量”的情况下，长度约束的理想曲线流应该允许进行更直接的分析。在本文中，我们表明确实如此，合适的初始数据提供了一直存在的流量，并将其平稳地收敛到与初始曲线相同长度和绕组数的多重覆盖圆圈。
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.
