Perturbed, Genus One Scherk Surfaces and their limits
The singly periodic, genus one helicoid is conjectured to be the limit of a one parameter family of doubly periodic minimal surfaces referred to as Perturbed Genus One Scherk Surfaces. Using elementary elliptic function theory, 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 then verify the conjecture.
Douglas, Casey. "Perturbed, Genus One Scherk Surfaces and their limits." (2009) Diss., Rice University. https://hdl.handle.net/1911/61835.