Topological criteria for schlichtness

TL;DR

This paper introduces new topological criteria to determine the schlichtness of envelopes of holomorphy, extending previous results and providing generalizations in complex analysis.

Contribution

It presents two sufficient topological conditions for schlichtness, generalizes Hammond's result in dimension 2, and extends Royden's theorem.

Findings

Two new criteria for schlichtness based on topology

Generalization of Hammond's result in dimension 2

Extension of Royden's theorem

Abstract

We give two sufficient criteria for schlichtness of envelopes of holomorphy in terms of topology. These are weakened converses of results of Kerner and Royden. Our first criterion generalizes a result of Hammond in dimension 2. Along the way we also prove a generalization of Royden's theorem.