The Lawson surfaces are determined by their symmetries and topology

TL;DR

This paper proves that Lawson surfaces in the three-sphere are uniquely characterized by their symmetries and topology, establishing their rigidity among minimal surfaces with the same genus.

Contribution

It demonstrates that Lawson surfaces are uniquely determined by their symmetries and genus, confirming their classification among minimal surfaces in the three-sphere.

Findings

Lawson surfaces are uniquely determined by their symmetries and genus.

Any minimal surface with Lawson symmetries and same genus is congruent to a Lawson surface.

The result confirms the rigidity of Lawson surfaces in the three-sphere.

Abstract

We prove that a closed embedded minimal surface in the round three-sphere which satisfies the symmetries of a Lawson surface and has the same genus is congruent to the Lawson surface.