ON THE SHORTENING RATE OF COLLECTIONS OF PLANE CONVEX CURVES BY THE AREA-PRESERVING MEAN CURVATURE FLOW
ON THE SHORTENING RATE OF COLLECTIONS OF PLANE CONVEX CURVES BY THE AREA-PRESERVING MEAN CURVATURE FLOW
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DOI：
10.1137/080721261
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发表时间：
2010-01-01
影响因子：
2
通讯作者：
Dai, Shibin
中科院分区：
文献类型：
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作者：
Dai, Shibin
保面积平均曲率流可以用来模拟一些相变。在几何上，在二维情况下，它们分别描述了作为分离两相的界面的曲线的缩短，同时保留每个相的面积。缩放参数表明，在保持面积的平均曲率流下，重新缩放的总曲线长度（L）随波浪线（t）以类似于ct（-1/2）的时间幂律（L）随波浪线（t）减小，其中c是正常数。本文考虑了一组互不相交的光滑凸平面曲线的演化，证明了（L）在波浪线上的衰减率的时均下界满足上述幂律，并得到了系数常数c对曲线形状的依赖关系.
Area-preserving mean curvature flows can be used to model some phase transitions. Geometrically, in the two-dimensional case, they describe the shortening of the curves that are interfaces separating the two phases while preserving the areas of each phase, respectively. Scaling arguments suggest that under the area-preserving mean curvature flow, the rescaled total curve length (L) over tilde (t) decreases as a temporal power law (L) over tilde (t) similar to ct(-1/2), where c is a positive constant. In this paper, we consider the evolution of a collection of nonintersecting smooth convex plane curves, prove a time-averaged lower bound of the decay rate of (L) over tilde which exhibits the aforementioned power law, and get the dependence of the coefficient constant c on the curve shapes.