Abstract
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.
Citation
Casey Douglas. "Genus one Scherk surfaces and their limits." J. Differential Geom. 96 (1) 1 - 59, January 2014. https://doi.org/10.4310/jdg/1391192691
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