Lawson's genus two minimal surface and meromorphic connections

Abstract

We investigate the Lawson genus $2$ surface by methods from integrable system theory. We prove that the associated family of flat connections comes from a family of flat connections on a $4-$punctured sphere. We describe the symmetries of the holonomy and show that it is already determined by the holonomy around one of the punctures. We show the existence of a meromorphic DPW potential for the Lawson surface which is globally defined on the surface. We determine this potential explicitly up to two unknown functions depending only on the spectral parameter.

References in corpus (1)

• Unitarization of monodromy representations and constant mean curvature trinoids in 3-dimensional space forms

Cited by in corpus (2)

• Complete families of embedded high genus CMC surfaces in the 3-sphere (with an appendix by Steven Charlton)
• Area Estimates for High genus Lawson surfaces via DPW