Evolution problems in geometric analysis

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dc.contributor.advisorHardt, Robert M.en_US
dc.creatorCheng, Xiaoxien_US
dc.date.accessioned2009-06-04T00:16:26Zen_US
dc.date.available2009-06-04T00:16:26Zen_US
dc.date.issued1991en_US
dc.description.abstractThis thesis studies problems derived from nonlinear partial differential equations of parabolic type. Part I. A mass reducing flow for integral currents. A mass reducing flow of integral current is constructed. The current flow has the property that it is Holder continuous under the flat norm and reduces the mass of the initial current while keeping the boundary fixed. Part II. Estimate of singular set of the evolution problems for harmonic maps. Let $u$: ${\cal M}$ $\times$ R$\sb+$ $\to$ ${\cal N}$ be a weak solution to the evolution problem for harmonic maps. We prove that the singular set of $u$ has at most finite $m$ $-$ 2 dimensional Hausdorff measure on each time slice ${\cal M}$ $\times$ $\{t\}$.en_US
dc.format.extent39 p.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.callnoThesis Math. 1991 Chengen_US
dc.identifier.citationCheng, Xiaoxi. "Evolution problems in geometric analysis." (1991) Diss., Rice University. <a href="https://hdl.handle.net/1911/16430">https://hdl.handle.net/1911/16430</a>.en_US
dc.identifier.urihttps://hdl.handle.net/1911/16430en_US
dc.language.isoengen_US
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.en_US
dc.subjectMathematicsen_US
dc.titleEvolution problems in geometric analysisen_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentMathematicsen_US
thesis.degree.disciplineNatural Sciencesen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelDoctoralen_US
thesis.degree.nameDoctor of Philosophyen_US
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