On meromorphic functions whose image has finite spherical area
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.