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dc.contributor.advisorToro, Tatianaen_US
dc.contributor.authorLewis, Stephenen_US
dc.date.accessioned2014-10-13T16:56:57Z
dc.date.available2014-10-13T16:56:57Z
dc.date.submitted2014en_US
dc.identifier.otherLewis_washington_0250E_13733.pdfen_US
dc.identifier.urihttp://hdl.handle.net/1773/26118
dc.descriptionThesis (Ph.D.)--University of Washington, 2014en_US
dc.description.abstractIn this thesis we develop the theory of Local Set Approximation (LSA), a framework which arises naturally from the study of sets with singularities. That is, we describe the local structure of a set A in Euclidean space through studying a class of sets S which approximates A well in small balls. We will give two interpretations LSA in Chapters 2 and 3. If in small balls B(x; r), our set A is close to some nice model set S, the approximation is unilateral. On the other hand, if in small balls B(x; r), our set A is close to S and S is close to A, the approximation is bilateral. Both of these models appear naturally in areas of geometric measure theory such as area minimizers, mass minimizers, free boundary, and regularity of measures. In Chapters 4 and 5, we give applications of local set approximation to the study of asymptotically optimally doubling measures.en_US
dc.format.mimetypeapplication/pdfen_US
dc.language.isoen_USen_US
dc.rightsCopyright is held by the individual authors.en_US
dc.subjectMeasure; Set Approximationen_US
dc.subject.otherMathematicsen_US
dc.subject.othermathematicsen_US
dc.titleLocal Set Approximation: Infinitesimal to Local Theorems for Sets in Euclidean Space and Applicationsen_US
dc.typeThesisen_US
dc.embargo.termsOpen Accessen_US


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