Lawson's genus two minimal surface and meromorphic connections
Differential Geometry
2013-10-22 v1
Abstract
We investigate the Lawson genus 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 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.
Keywords
Cite
@article{arxiv.1009.5487,
title = {Lawson's genus two minimal surface and meromorphic connections},
author = {Sebastian Heller},
journal= {arXiv preprint arXiv:1009.5487},
year = {2013}
}