On meromorphic functions whose image has finite spherical area

Oleg Ivrii

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arXiv · 2201.12227

On meromorphic functions whose image has finite spherical area

Oleg Ivrii

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Abstract

In this paper, 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.

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Oleg Ivrii. 2022-01-28. On meromorphic functions whose image has finite spherical area. https://arxiv.org/abs/2201.12227

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