Asymptotic closeness to limiting shapes for expanding embedded plane curves
Asymptotic closeness to limiting shapes for expanding embedded plane curves
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DOI：
10.1007/s00222-005-0449-9
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发表时间：
2005-06
影响因子：
3.1
通讯作者：
Dong-Ho Tsai
中科院分区：
文献类型：
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作者：
Dong-Ho Tsai
证明了对于嵌入或凸平面曲线展开，展开曲线γt与某些展开圆Ct(半径为r(T))之间的支撑函数之差(x，t)-r(T)有其渐近形→∞.此外，等周差L2-4π是减小的，并且收敛到一个常数，即膨胀速度渐近为常数，且初始曲线不是圆。对于凸初曲线，如果展开速度是渐近无穷的，则L2-4πA减小到，并且存在γt的渐近展开中心。
We show that for embedded or convex plane curves expansion, the differenceu(x,t)-r(t) in support functions between the expanding curves γtand some expanding circlesCt(with radiusr(t)) has its asymptotic shape ast→∞. Moreover the isoperimetric differenceL2-4πAis decreasing and it converges to a constantif the expansion speed is asymptotically a constant and the initial curve is not a circle. For convex initial curves, if the expansion speed is asymptotically infinite, thenL2-4πAdecreases toand there exists an asymptotic center of expansion for γt.