A characterisation of the Hoffman-Wohlgemuth surfaces in terms of their symmetries

TL;DR

This paper characterizes Hoffman-Wohlgemuth minimal surfaces with certain symmetry conditions, providing a geometric proof that links their symmetries to their classification among embedded singly periodic minimal surfaces.

Contribution

It offers a new geometric proof connecting symmetry hypotheses to the classification of Hoffman-Wohlgemuth surfaces, enhancing understanding of their geometric properties.

Findings

Weak symmetry conditions imply congruence with Hoffman-Wohlgemuth surfaces.

The proof provides valuable geometric insights into these minimal surfaces.

Symmetry plays a key role in classifying embedded singly periodic minimal surfaces.

Abstract

For an embedded singly periodic minimal surface M with genus bigger than or equal to 4 and annular ends, some weak symmetry hypotheses imply its congruence with one of the Hoffman-Wohlgemuth examples. We give a very geometrical proof of this fact, along which they come out many valuable clues for the understanding of these surfaces.