TY - JOUR

T1 - A schwarz lemma for meromorphic functions and estimates for the hyperbolic metric

AU - Solynin, Alexander Yu

N1 - Copyright:
Copyright 2010 Elsevier B.V., All rights reserved.

PY - 2008/9

Y1 - 2008/9

N2 - We prove a generalization of the Schwarz lemma for meromorphic functions f mapping the unit disk D onto Riemann surfaces ℛ with bounded in mean radial distances from f(0) to the boundary of ℛ. A newvariant of the Schwarz lemma is also proved for the Carathèodory class of analytic functions having positive real part in D. Our results lead to several improved estimates for the hyperbolic metric.

AB - We prove a generalization of the Schwarz lemma for meromorphic functions f mapping the unit disk D onto Riemann surfaces ℛ with bounded in mean radial distances from f(0) to the boundary of ℛ. A newvariant of the Schwarz lemma is also proved for the Carathèodory class of analytic functions having positive real part in D. Our results lead to several improved estimates for the hyperbolic metric.

UR - http://www.scopus.com/inward/record.url?scp=77950630964&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-08-09309-X

DO - 10.1090/S0002-9939-08-09309-X

M3 - Article

AN - SCOPUS:77950630964

VL - 136

SP - 3133

EP - 3143

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 9

ER -