Minimising weighted mean distortion : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Mathematics at Massey University, Albany, New Zealand

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dc.contributor.authorMcKubre-Jordens, Maarten Nicolaas
dc.date.accessioned2010-05-03T00:43:13Z
dc.date.availableNO_RESTRICTIONen_US
dc.date.available2010-05-03T00:43:13Z
dc.date.issued2009
dc.description.abstractThere has been considerable recent interest in geometric function theory, nonlinear partial differential equations, harmonic mappings, and the connection of these to minimal energy phenomena. This work explores Nitsche's 1962 conjecture concerning the nonexistence of harmonic mappings between planar annuli, cast in terms of distortion functionals. The connection between the Nitsche problem and the famous Grötzsch problem is established by means of a weight function. Traditionally, these kinds of problems are investigated in the class of quasiconformal mappings, and the assumption is usually made a priori that solutions preserve various symmetries. Here the conjecture is solved in the much wider class of mappings of finite distortion, symmetry-preservation is proved, and ellipticity of the variational equations concerning these sorts of general problems is established. Furthermore, various alternative interpretations of the weight function introduced herein lead to an interesting analysis of a much wider variety of critical phenomena -- when the weight function is interpreted as a thickness, density or metric, the results lead to a possible model for tearing or breaking phenomena in material science. These physically relevant critical phenomena arise, surprisingly, out of purely theoretical considerations.en_US
dc.identifier.urihttp://hdl.handle.net/10179/1279
dc.language.isoenen_US
dc.publisherMassey Universityen_US
dc.rightsThe Authoren_US
dc.subjectWeighted mean distortionen_US
dc.subjectWeight functionen_US
dc.subjectMathematicsen_US
dc.subject.otherFields of Research::230000 Mathematical Sciences::230100 Mathematicsen_US
dc.titleMinimising weighted mean distortion : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Mathematics at Massey University, Albany, New Zealanden_US
dc.typeThesisen_US
massey.contributor.authorMcKubre-Jordens, Maarten Nicolaas
thesis.degree.disciplineMathematicsen_US
thesis.degree.grantorMassey Universityen_US
thesis.degree.levelDoctoralen_US
thesis.degree.levelDoctoralen
thesis.degree.nameDoctor of Philosophy (Ph.D.)en_US
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