Constant mean curvature surfaces and Heun's differential equations

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dc.check.embargoformatEmbargo not applicable (If you have not submitted an e-thesis or do not want to request an embargo)en
dc.check.infoNot applicableen
dc.check.opt-outNot applicableen
dc.check.reasonNot applicableen
dc.check.typeNo Embargo Required
dc.contributor.advisorKilian, Martinen
dc.contributor.authorMota, Eduardo
dc.contributor.funderUniversity College Corken
dc.date.accessioned2019-08-22T11:12:35Z
dc.date.available2019-08-22T11:12:35Z
dc.date.issued2019
dc.date.submitted2019
dc.description.abstractThis thesis is concerned with the problem of constructing surfaces of constant mean curvature with irregular ends by using the class of Heun’s Differential Equations. More specifically, we are interested in obtaining immersion of punctured Riemann spheres into three dimensional Euclidean space with constant mean curvature. These immersions can be described by a Weierstrass representation in terms of holomorphic loop Lie algebra valued 1-forms. We describe how to encode each of the differential equations in Heun’s family in the Weierstrass representation. Next, we investigate monodromy problems for each of the cases in order to ensure periodicity of all the resulting immersions. This allows us to find four families of surfaces with constant mean curvature and irregular ends. These families can be described as trinoids, cylinders, perturbed Delaunay surfaces and planes. Finally, we study some symmetry properties of these groups of surfaces.en
dc.description.statusNot peer revieweden
dc.description.versionAccepted Version
dc.format.mimetypeapplication/pdfen
dc.identifier.citationMota, E. 2019. Constant mean curvature surfaces and Heun's differential equations. PhD Thesis, University College Cork.en
dc.identifier.endpage129en
dc.identifier.urihttps://hdl.handle.net/10468/8375
dc.language.isoenen
dc.publisherUniversity College Corken
dc.relation.projectUniversity College Cork (School of Mathematical Sciences)en
dc.rights© 2019, Eduardo Mota.en
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/en
dc.subjectDifferential geometryen
dc.subjectTheory of surfacesen
dc.subjectMean curvatureen
dc.subjectOrdinary differential equationsen
dc.subjectSingularitiesen
dc.thesis.opt-outfalse
dc.titleConstant mean curvature surfaces and Heun's differential equationsen
dc.typeDoctoral thesisen
dc.type.qualificationlevelDoctoralen
dc.type.qualificationnamePhDen
ucc.workflow.supervisorm.kilian@ucc.ie
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