We study an important subclass of quasicircles, namely, symmetric quasicircles. Several characterizations for quasicircles, such as the reverse triangle inequality, the M -condition and the quasiconformal extension property, have been extended to symmetric quasicircles by Becker and Pommerenke and by Gardiner and Sullivan. In this paper we establish several relations among various domain constants such as quasiextremal distance constants, (local) reflection constants and (local) extension constants for this class. We also give several characterizations for symmetric quasicircles such as the strong quadrilateral inequality and the strong extremal distance property. They correspond to the quadrilateral inequality and the extremal distance property for quasicircles.

By studying the mapping by heights for quadratic differentials introduced by Strebel, some relations have been established between the maximal norm sequence for quasisymmetric functions and the Hamilton sequence for extremal quasiconformal mappings in the unit disk. Consequently it is proved that a Hamilton sequence is only determined by e quasisymmetric function.

In this paper, some results on removable sets of entire and meromorphic functions in the sense of borel Theorem are obtained. Among them we prove that there exists a se-quence of discs (Dn) with radii tending to the infinity such that for any entire function f(z)with a positiv eand finite order, Borel Theorem always holds in C\∪∞n=1Dn.

本文研究了亚纯函数的不动点与拟正规的关系，得到了以下结果：设F是区域D内的亚纯函数族，q是一个非负整数。如果对任意的f∈F存在自然数k=k（f）>1，使得f的k次迭代fk在D内最多有q个不动点，则F是D内阶至多为max{4,q+3}的拟正规族。