P-harmonic morphisms, minimal foliations, and conformal deformations of metrics /

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dc.contributor.advisorWalschap, Gerard,en_US
dc.contributor.authorOu, Ye-lin.en_US
dc.date.accessioned2013-08-16T12:19:47Z
dc.date.available2013-08-16T12:19:47Z
dc.date.issued2005en_US
dc.description.abstractIn this dissertation, we study p-harmonic morphisms and its interaction with minimal foliations and conformal deformations of metrics. We give several methods to construct non-trivial p-harmonic morphisms via conformal deformations of metric on the domain and/or target manifold. We classify polynomial p-harmonic morphisms between Euclidean spaces and holomorphic p-harmonic morphisms between complex Euclidean spaces. We find three applications of p-harmonic morphisms including applications to the study of biharmonic morphisms and in showing the existence of harmonic 3-sphere in a general Riemannian manifold with noncontractible universal covering space. Finally, we give links between p-harmonicity of functions and the minimality of their level hypersurfaces or of their vertical graphs. We prove that the foliation defined by the level hypersurfaces of a submersive p-harmonic function or by the vertical graphs of a harmonic function can always be turned into a minimal foliation via a suitable conformal deformation of metric.en_US
dc.format.extentviii, 67 leaves ;en_US
dc.identifier.urihttp://hdl.handle.net/11244/858
dc.noteSource: Dissertation Abstracts International, Volume: 66-02, Section: B, page: 0936.en_US
dc.noteAdviser: Gerard Walschap.en_US
dc.subjectRiemannian manifolds.en_US
dc.subjectMathematics.en_US
dc.subjectGeometry, Differential.en_US
dc.subjectHarmonic morphisms.en_US
dc.thesis.degreePh.D.en_US
dc.thesis.degreeDisciplineDepartment of Mathematicsen_US
dc.titleP-harmonic morphisms, minimal foliations, and conformal deformations of metrics /en_US
dc.typeThesisen_US
ou.groupCollege of Arts and Sciences::Department of Mathematics
ou.identifier(UMI)AAI3163314en_US

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