拟对称函数增长阶的估值

ESTIMATE ON GROWTH ORDER OF QUASI-SYMMETERIC FUNCTION

设Ｇ_１与Ｇ_２是由光滑Ｔｏｒｄａｎ闭曲线界成的区域，ｆ为Ｇ_１到Ｇ_２的μ（ｚ）－同胚，当ｆ的平均伸长函数由对数函数控制时，则ｆ可拓扑地延拓到边界，记边界函数为 ｈ，本文引进了由 ｈ生成的拟对称函数ρ_ｈ，利用模理论及极值长度方法，我们估计了拟对称函数的增长阶，得到一个双向不等式。

Let G_1 and G_2 be two domains bounded by smooth Jordan closed Curves, f be aμ(z)- homeomorphism from G_1 onto G_2. When the mean dilatation of f is Controled by logarithm founction, f can be topologically extend to the boundary. Denote the boundary function by h. In this paper, wi introduce qasi-symmetric function ρ_h which is generated by function h. Using modulus theory and extremal length method, We estimate the growt order of quasi-symmetric function adn obtain an inequality of both direction.