利用模函数估计拟共形映照的偏差函数

摘要

推广一个关于环形区域模函数μ(r)的不等式,对拟共形映照的偏差函数λ(K)作出更精确的估计,得到λ(K)=1/16exK-1/2+5/4e-πK-31/8e-3πK+27/2e-5πK-c(K)e-7πK,其中,633/16＜c(K)＜321/8.%We extend an inequality for the module functionμ(r) defined in a double ring domain,using this result,we obtain better estimate for quasiconformal distortion function λ (K).We prove that λ(K)=1/16 eπK-1/2 + 5/4e-πK-31/8e-3πK+27/2e-5πK-c(K)e-7πK,where 633/16＜c(K)＜321/8.