Area Estimates for High genus Lawson surfaces via DPW

TL;DR

This paper introduces a new method to prove the existence of high genus Lawson surfaces by deforming DPW potentials, and provides area estimates related to their genus.

Contribution

It presents a novel existence proof for high genus Lawson surfaces using DPW potential deformation, with area estimates as a key result.

Findings

Existence of high genus Lawson surfaces established via deformation of DPW potentials.

Derived area estimates for Lawson surfaces in relation to their genus.

Method offers a new approach to studying high genus minimal surfaces.

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 $g=m k \gg1$.