Asymptotic estimates for moduli of extremal rings (Q1058011)

For \(n\geq 2\) 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 [-a,a] along the \(x_ 1\)-axis. Significant lower and upper limits as n tends to \(\infty\) are obtained for the expressions \[ mod R_ n(a)-n+ \log n\quad and\quad n^{-n} mod R_ n(a)^ n, \] where mod denotes the conformal modulus.