ASYMPTOTIC ESTIMATES FOR MODULI OF EXTREMAL RINGS

Abstract

For n ≥ 2 and 0 < a < 1 let {R_n}(a) denote the extremal ring domain consisting of the unit ball in n-space minus the closed slit left[ { - a, a} \ ight] along the {x_1}-axis. Significant lower and upper limits as n tends to ∞ are obtained for the expressions
\bmod {R_n}(a) - n + {1 \over 2}log n
and
{n^{1/2 - n}}\bmod {R_n}{(a)^n},
where mod denotes the conformal modulus.