多连通区域上的Bloch常数

<正> 本文可以看作1]文的一个应用,在这里将提供一个关于多连通区域的 Bloch 常数的估计的普遍方法.并且特别以于二连通区域的 Bloch 常数进行了具体的估计.

ON THE BLOCH CONSTANT FOR MULTIPLY CONNECTED REGIONS

Let D be a bounded multiply connected region in z-plane.The curvatureof Bergman metric of this region takes the minimum value τ_α at z=α.Let w=f(z)be an analytic function in D with(?),which mapsD onto D_f in w-plane.The object of the present note is to prove that D_f must contain a circlewith radius(?)where T_b is the value of the Bergman metric T of theregion D at z=b.Further,if the function f(z)is simple in D,then D_f mustcontain a circle with radius(?)