Axial minimal surfaces in S^2 x R are helicoidal

TL;DR

This paper proves that certain minimal surfaces in S^2 x R with specific properties are necessarily helicoids, establishing a classification result for these geometric objects.

Contribution

It demonstrates that complete, properly embedded minimal surfaces in S^2 x R containing a line are asymptotic to helicoids, and annular ones are exactly helicoids.

Findings

Surfaces with a line are asymptotic to helicoids

Annular minimal surfaces in S^2 x R are helicoids

Classification of minimal surfaces with finite topology in S^2 x R

Abstract

We prove that if a complete, properly embedded, finite-topology minimal surface in S^2 x R contains a line, then its ends are asymptotic to helicoids, and that if the surface is an annulus, it must be a helicoid.