Area Estimates for High genus Lawson surfaces via DPW

Abstract

Starting at a saddle tower surface, we give a new existence proof of the Lawson surfaces ${\xi }_{m,k}$ of high genus by deforming the corresponding DPW potential. As a byproduct, we obtain for fixed $m$ estimates on the area of ${\xi }_{m,k}$ in terms of their genus $g=mk\gg 1$.

33 pages, 2 figures, accepted for publication in Journal of Differential Geometry