Higher genus maxfaces with Enneper end

TL;DR

This paper proves the existence of new higher-genus maxfaces with Enneper ends, which are distinct from known minimal surfaces, and analyzes their singularity structures.

Contribution

It introduces novel higher-genus maxfaces with Enneper ends that are not related to existing minimal surfaces, expanding the understanding of maxface geometry.

Findings

Existence of new higher-genus maxfaces with Enneper ends

Singularities are located away from the ends

Systematic investigation of singularity nature

Abstract

We have proven the existence of new higher-genus maxfaces with Enneper end. These maxfaces are not the companions of any existing minimal surfaces, and furthermore, the singularity set is located away from the ends. The nature of the singularities is systematically investigated.