On meromorphic functions whose image has finite spherical area
Volume 272 / 2023
Studia Mathematica 272 (2023), 121-137
MSC: Primary 30D45; Secondary 30C62.
DOI: 10.4064/sm220618-19-3
Published online: 7 June 2023
Abstract
We study meromorphic functions on a domain $\Omega \subset \mathbb C$ whose image has finite spherical area, counted with multiplicity. The paper is composed of two parts. In the first part, we show that the limit of a sequence of meromorphic functions is naturally defined on $\Omega $ union a tree of spheres. In the second part, we show that a set $E \subset \Omega $ is removable if and only if it is negligible for extremal distance.
