次带状曲线的拟等距扩张性质

The QuasiiSometric Extension Property of Subribbon Curves

该文得到了如下结果:若C是c-次带状曲线,则C上的L-拟等距映射φ在R^2上有M-拟等距扩张g的充要条件是φ(C)是c＇-次带状曲线,其中M=M(c,c＇,L)为常数。从而给出了另外一类具有拟等距扩张性质但不是拟圆周的Jordan曲线,这推广了F.W.Gehring的结论。

This paper obtains the following result: If C is c - subribboncurve, then each L - quasiisometry φ of C has an M -quasiisometric extension toR^2 if and only if φ(C) is C' - subribbon curve, where M = M(c,c' , L) is con-stant. Thereby,the paper gives a class of Jordan curves which have the quasi-isometric extension property but are not quasicircles,and extend the F. W.Gehring's result.