Beurling-Ahlfors扩张的伸张函数与ID-同胚

Dilatation Function of Beurling-Ahlfors Extension and ID-Homeomorphism

本文研究实轴上同胚在上半平面的扩张.利用拟对称函数ρ对伸张函数D作了较精细的估计.同时借助于诱导的边界函数对D、ρ在边界附近的性质作了进一步刻划.作为应用,我们分别给出上半平面存在ID-同胚扩张和IID-同胚扩张的充分条件.

In this paper, we study the extensions on the upper half plane of the homeo-morphisms on the real axis.Using the quasisymmetric function, we get a relatively fine estimate of the dilatation function. In the meantime, we give a further characterization on D and p near the boundary by an induced boundary function. As applications, sufficient conditions of the existence of ID homeomorphism and IID homeomorphism are respectively presented.