Open Access
January 2014 Genus one Scherk surfaces and their limits
Casey Douglas
J. Differential Geom. 96(1): 1-59 (January 2014). DOI: 10.4310/jdg/1391192691


The singly periodic, genus one helicoid was conjectured to be the limit of a one parameter family of doubly periodic minimal surfaces referred to as Perturbed Genus One Scherk Surfaces. Using elliptic functions, we show such surfaces exist, solving a two-dimensional period problem by perturbing a one-dimensional problem. Using flat structures associated to these minimal surfaces, we verify the conjecture.


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Casey Douglas. "Genus one Scherk surfaces and their limits." J. Differential Geom. 96 (1) 1 - 59, January 2014.


Published: January 2014
First available in Project Euclid: 31 January 2014

zbMATH: 1293.53010
MathSciNet: MR3161384
Digital Object Identifier: 10.4310/jdg/1391192691

Rights: Copyright © 2014 Lehigh University

Vol.96 • No. 1 • January 2014
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