Wolf, Michael2011-07-252011-07-252009Douglas, Casey. "Perturbed, Genus One Scherk Surfaces and their limits." (2009) Diss., Rice University. <a href="https://hdl.handle.net/1911/61835">https://hdl.handle.net/1911/61835</a>.https://hdl.handle.net/1911/61835The 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.application/pdfengCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.MathematicsThesisTHESIS MATH. 2009 DOUGLAS