Exploring the space of compact symmetric CMC surfaces

TL;DR

This paper numerically explores the moduli space of Lawson symmetric constant mean curvature surfaces in the 3-sphere, starting from Delaunay tori and using the generalized Whitham flow to map out higher genus surfaces.

Contribution

It introduces a numerical method to explore the moduli space of symmetric CMC surfaces in the 3-sphere, extending known surfaces via the generalized Whitham flow.

Findings

Mapped the moduli space of symmetric CMC surfaces for genus > 1

Connected Delaunay tori to higher genus surfaces through flow

Provided new insights into the structure of CMC surface moduli space

Abstract

We map out the moduli space of Lawson symmetric constant mean curvature surfaces in the 3-sphere of genus $g>1$ by flowing numerically from Delaunay tori with even lobe count via the generalized Whitham flow.