Equicontinuous families of meromorphic mappings with values in compact complex surfaces

TL;DR

This paper proves that equicontinuous families of meromorphic mappings from a bidisc to a compact complex surface have uniformly bounded graph volumes near the boundary.

Contribution

It establishes a volume boundedness result for families of meromorphic mappings with boundary equicontinuity into compact complex surfaces.

Findings

Volumes of graphs are locally uniformly bounded near the boundary.

Equicontinuity in a neighborhood of the boundary implies volume control.

Results contribute to understanding the boundary behavior of meromorphic families.

Abstract

We prove that a family of meromorphic mappings from a bidisc to a compact complex surface, which are equicontinuous in a neighborhood of the boundary of the bidisc, has the volumes of its graphs locally uniformly bounded.