Rn中Gr(o)tzsch环的共形模的一个不等式

摘要

Let r′= 1-r2 and Mn(r) be the (conformal) modulus of the Gr(o)tzsch Ring in the quasiconformal theory in Rn ,for n≥3 and r∈(0 ,1) .In this paper ,a double inequality is obtained for the function H(r)≡ r′2 Mn(r) Mn(r′)n-1 + r2 Mn(r′)Mn(r)n-1 ,thus improving known bounds for H(r) ,and correcting an error in the proof of a related inequality for H (r) which was given in a monograph by G .D .Anderson ,M .K .Vamanamurthy and M . Vuorinen .%设Mn(r)为n维拟共形理论中的Gr(o)tzsch环RG,n(1/r)的模,r′=1-r2,其中0