Area Estimates for High genus Lawson surfaces via DPW

2019/07/16 by Heller, Lynn, Heller, Sebastian, Traizet, Martin · 1 citation
#53A10 #53C42 #53C43 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1907.07139

Abstract

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

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• A new family of minimal surfaces of even genus in the three-dimensional sphere

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