关于实轴自同胚的延拓

On Extensions of Self-homeomorphism of the Real Line

逐点伸缩偏差满足一定条件时,实轴保向自同胚可以由Beurling-Ahlfors扩张连续延拓为David映射.利用修改的三角剖分扩张,本文给出实轴保向自同胚连续延拓为David映射的另一个充分条件,该条件去掉了保向自同胚的一个限制.

A sense-preserving self-homeomorphism of the real line can be continuously extended to a David mapping by Beurling-Ahlfors extension if the scale-wise distortion satisfies some conditions.By using a modified triangulation extension,another sufficient condition,for which a sense-preserving self-homeomorphism of the real line can be continuously extended to a David mapping,is given.This result removes one restriction on the sense-preserving selfhomeomorphism.