Uniformization of surfaces with boundary and the application to the triple junction surfaces with negative Euler characteristic

TL;DR

This paper extends the uniformization theorem to surfaces with boundary and applies it to triple junction surfaces with negative Euler characteristic, enhancing understanding of their conformal structures.

Contribution

It introduces a weak uniformization result for triple junction surfaces, broadening the scope of conformal geometry in complex surface analysis.

Findings

Established weak uniformization for triple junction surfaces

Extended uniformization results to surfaces with boundary

Provided insights into conformal structures of complex surfaces

Abstract

The conformal structure on minimal surfaces plays a key role in studying the properties of minimal surfaces. Here we extend the results of uniformization of surfaces with boundary to get the (weak) uniformization results for triple junction surfaces.