On meromorphic functions whose image has finite spherical area

2022/01/28 by Ivrii, Oleg · 1 citation
#Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2201.12227

Abstract

In this paper, we study meromorphic functions on a domain Ω⊂ 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 Ω union a tree of spheres. In the second part, we show that a set E ⊂ Ω is removable if and only if it is negligible for extremal distance.

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