关于凸像共形映照的掩蔽性质

<正> 1.设G是复数W平面上的一个凸形区域.假如通过G的一个境界点有一个圆周把G合在它的内部,那末这个圆周是 G 在此境界点的支持圆周.设在 G 的每一个境界点都有一个半径不超过ρ(ρ>0)的支持圆周,并且有一个点,其支持圆周的半径不能小于ρ,那末称 G 是一由半径为ρ的圆所支持的凸形区域.我们又简称这种区域为支持半径为ρ的区域.当ρ=∞时圆周化成直线,每一凸形区域都为一个半平面所支持.

SOME COVERING PROPERTIES OF CONVEX DOMAINS IN THE THEORY OF CONFORMAL MAPPING

Let D be a convex domain in w-plane.Let w=0 belong to D,and letthe inner radius of D with respect to w= 0 is unity.Suppose that forevery boundary point w of D,there exists a circle with radius ρ(a fixed number)passing through w and containing D.Denote by C_ρ,the familyof all such domains D.Let D ∈C_ρ,w_ν ∈D,ν = 1,2,…,n be n points suchthat(?)Write(?)In the present note we have proved the followingTheorem:If(?)Then (?)where x denotes the root of equation(?)such that 0