# Lawson correspondence for minimal and constant mean curvature surfaces

## Université Paris-Est Marne-la-Vallée

Lawson correspondence between minimal surfaces in \(\mathbb{S}^3\) and constant mean curvature (CMC) surfaces in \(\mathbb{R}^3\) is instrumental in building examples of surfaces, but also reveals a lot about the structure of underlying PDEs. In discrete geometry, simple definitions of CMC surfaces are not obvious (many have been given) and an analog to Lawson correspondence has eluded researchers for a long time. We will present here a natural and computation-friendly definition, based on Lax pairs, which showcases the analogy between the two types of surfaces, as well as proposes a construction method. We will try to outline the similarities and differences between the smooth and discrete realms. Joint work with Alexander Bobenko (TU Berlin)