Deformations of symmetric CMC surfaces in the 3-sphere

TL;DR

This paper numerically constructs constant mean curvature (CMC) deformations of Lawson minimal surfaces in the 3-sphere using spectral curve and DPW methods, advancing understanding of their geometric properties.

Contribution

It introduces a numerical approach to deform Lawson minimal surfaces into CMC surfaces in spaceforms, employing spectral curve and DPW techniques for the first time.

Findings

Successfully constructed CMC deformations of Lawson surfaces.

Demonstrated the effectiveness of spectral curve and DPW methods in this context.

Provided new insights into the geometry of CMC surfaces in the 3-sphere.

Abstract

In this paper we numerically construct CMC deformations of the Lawson minimal surfaces $\xi_{g,1}$ using a spectral curve and a DPW approach to CMC surfaces in spaceforms.