Projective Hulls and Characterizations of Meromorphic Functions

TL;DR

This paper explores conditions that characterize holomorphic and meromorphic functions within the unit disk using weak maximum principles, inspired by recent theoretical developments in complex analysis and projective hulls.

Contribution

It introduces new characterizations of holomorphic and meromorphic functions based on weak maximum principles, connecting classical analysis with projective hull theory.

Findings

Characterizations of functions via weak maximum principles

Connections between classical complex analysis and projective hulls

Inspired by recent advances in the theory of projective hulls

Abstract

We give conditions characterizing holomorphic and meromorphic functions in the unit disk of the complex plane in terms of certain weak forms of the maximum principle. Our work is directly inspired by recent results of John Wermer, and by the theory of the projective hull of a compact subset of complex projective space developed by Reese Harvey and Blaine Lawson.