The Second Main Theorem in the hyperbolic case

TL;DR

This paper extends Nevanlinna's theory to holomorphic maps from a disc, relevant for the study of foliations by Riemann surfaces, providing new insights into value distribution in hyperbolic contexts.

Contribution

It introduces a version of the Second Main Theorem for holomorphic maps from discs, advancing the understanding of value distribution in hyperbolic geometry.

Findings

Developed Nevanlinna theory for disc-source holomorphic maps

Applied results to foliations by Riemann surfaces

Enhanced understanding of hyperbolic value distribution

Abstract

We develop Nevanlinna's theory for a class of holomorphic maps when the source is a disc. Such maps appear in the theory of foliations by Riemann Surfaces.