非简单曲线的保长度流及其应用
A Length-Preserving Flow for Non-Simple Curves and Its Applications
摘要: 本文主要研究非简单曲线的保长度流及其应用，在该保长度流下，如果初始曲线是具有对称性的局部凸曲线，那么在演化过程中该曲线保持局部凸性和长度，且收敛到一个多重圆。作为该流的应用，可获得非简单曲线的等周不等式和对数型不等式。
Abstract:
This article mainly studies the length-preserving flow of non-simple curves and its applications. Under this flow, if the initial curve is a locally convex curve with symmetry, this curve is still locally convex and keeps length, and converges to a multiple circle. As an application of this flow, isop-erimetric inequality and logarithmic inequalities for non-simple curves can be obtained.
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