Perturbed, Genus One Scherk Surfaces and their limits

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dc.contributor.advisorWolf, Michael
dc.creatorDouglas, Casey
dc.date.accessioned2011-07-25T01:38:32Z
dc.date.available2011-07-25T01:38:32Z
dc.date.issued2009
dc.description.abstractThe 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.
dc.format.mimetypeapplication/pdf
dc.identifier.callnoTHESIS MATH. 2009 DOUGLAS
dc.identifier.citationDouglas, 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>.
dc.identifier.urihttps://hdl.handle.net/1911/61835
dc.language.isoeng
dc.rightsCopyright 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.
dc.subjectMathematics
dc.titlePerturbed, Genus One Scherk Surfaces and their limits
dc.typeThesis
dc.type.materialText
thesis.degree.departmentMathematics
thesis.degree.disciplineNatural Sciences
thesis.degree.grantorRice University
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy
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