Coordinate scans, compactness properties, and area minimization

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dc.contributor.advisorHardt, Robert M.en_US
dc.creatorPeterson, James Ernesten_US
dc.date.accessioned2009-06-04T08:08:19Zen_US
dc.date.available2009-06-04T08:08:19Zen_US
dc.date.issued2006en_US
dc.description.abstractIn the framework of geometric measure theory, we investigate compactness results and possible solutions of area-minimizing problems on surfaces using area functionals other than the traditional mass norm. These solutions will be of a relatively new class of objects called rectifiable coordinate scans. We begin by reviewing traditional theory and motivating problems for using non-mass area functionals. Next we set up the basic definitions and theorems, mostly in analogy to the classical theory of currents. Our major result is a rectifiable compactness theory which leads to solutions of Plateau-type problems for scans. Finally, we use our compactness results to construct a Holder continuous area-decreasing flow.en_US
dc.format.extent58 p.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.callnoTHESIS MATH. 2006 PETERSONen_US
dc.identifier.citationPeterson, James Ernest. "Coordinate scans, compactness properties, and area minimization." (2006) Diss., Rice University. <a href="https://hdl.handle.net/1911/18957">https://hdl.handle.net/1911/18957</a>.en_US
dc.identifier.urihttps://hdl.handle.net/1911/18957en_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.titleCoordinate scans, compactness properties, and area minimizationen_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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