We prove a generalization of the Schwarz lemma for meromorphic functions mapping the unit disk onto Riemann surfaces with bounded in mean radial distances from to the boundary of . A new variant of the Schwarz lemma is also proved for the Carathèodory class of analytic functions having positive real part in . Our results lead to several improved estimates for the hyperbolic metric.
|Journal||Proc. Amer. Math. Soc.|
|State||Published - Sep 2008|