A Generalized Hyperbolic Metric for Plane Domains
نویسندگان
چکیده
A plane domain Ω with more than one boundary point admits a hyperbolic metric and with respect to this metric, every holomorphic map of Ω into a subdomain X ⊆ Ω is a contraction. In this paper we define a new metric for the image domain X that is greater than or equal to the hyperbolic metric. Like the hyperbolic metric it has the property that any holomorphic map from Ω into X is a contraction. This metric has applications to random holomorphic iteration.
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