Minimal surfaces containing an epitrochoid as a geodesic

TL;DR

This paper proves that a complete minimal surface cannot contain a specific type of epitrochoid as a geodesic, contributing to the understanding of the geometric constraints of minimal surfaces.

Contribution

It establishes a new restriction on the geodesic curves that can exist on complete minimal surfaces, specifically ruling out certain epitrochoids.

Findings

Complete minimal surfaces cannot have certain epitrochoids as geodesics.

Provides a geometric constraint on minimal surfaces.

Advances understanding of the relationship between curves and minimal surfaces.

Abstract

We show a complete minimal immersion cannot have a certain kind of epitrochoid as a geodesic.