A Schwarz lemma for meromorphic functions and estimates for the hyperbolic metric

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Abstract

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.
Original languageEnglish
Pages (from-to)3133-3143
JournalProc. Amer. Math. Soc.
StatePublished - Sep 2008

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