Value-sharing of meromorphic functions on a Riemann surface

TL;DR

This paper investigates the value-sharing properties of two meromorphic functions defined on various types of Riemann surfaces, including compact surfaces, punctured surfaces, the unit disk, tori, and the complex plane.

Contribution

It provides new results on how two meromorphic functions share values across different classes of Riemann surfaces, extending classical value-sharing theories.

Findings

Results on value-sharing for meromorphic functions on compact Riemann surfaces

Extensions to non-compact surfaces like the punctured sphere and the complex plane

Insights into the behavior of meromorphic functions on tori and the unit disk

Abstract

We present some results on two meromorphic functions from S to the Riemann sphere sharing a number of values where S is a Riemann surface of one of the following types: compact, compact minus finitely many points, the unit disk, a torus, the complex plane.