The Beurling-Ahlfors’ extension is studied under relatively general conditions and its dilatation fonction is estimated. Particularly, the classic Deurling -Ahlfors’ theorem can be obtained under the M-condition.
文摘对于实轴上满足M条件的自同胚映射h(x),利用一系列积分不等式的精细估计,将相应问题转化为定义在一个凸五边形约束域G上伸张函数f(ξ,η)的估计式;然后根据f(ξ,η)的凸性和其在区域G 5个顶点上函数值的直接计算,从而得到了Beurling-A h lfors扩张映射φ(z)的伸张函数D的最优值估计:D≤2M.本文的证明不同于Lehtinen传统方法.
文摘The Beurling-Ahlfors’ extension is studied under relatively general conditions and its dilatation fonction is estimated. Particularly, the classic Deurling -Ahlfors’ theorem can be obtained under the M-condition.
