Limit Surfaces of Riemann Examples

TL;DR

This paper studies the limit surfaces of Riemann's minimal examples, showing they can converge to classical minimal surfaces like the helicoid, catenoid, or configurations of parallel planes.

Contribution

It characterizes the possible limit surfaces of Riemann's minimal examples, expanding understanding of their geometric behavior.

Findings

Limit surfaces include helicoid, catenoid, single plane, or infinite parallel planes.

Provides classification of limit behaviors for Riemann minimal surfaces.

Enhances understanding of the asymptotic geometry of these surfaces.

Abstract

The family of embedded, singly periodic minimal surfaces of Riemann have as limit-surfaces the helicoid, the catenoid, a single plane, or an infinite set of equally-spaced parallel planes.