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dc.contributor.advisorMitrea, Mariuseng
dc.contributor.authorBrigham, Dan, 1987-eng
dc.date.issued2011eng
dc.date.submitted2011 Springeng
dc.descriptionTitle from PDF of title page (University of Missouri--Columbia, viewed on May 26, 2011).eng
dc.descriptionThe entire thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file; a non-technical public abstract appears in the public.pdf file.eng
dc.descriptionThesis advisor: Dr. Marius Mitrea.eng
dc.descriptionIncludes bibliographical references.eng
dc.descriptionM.A. University of Missouri--Columbia 2011.eng
dc.description.abstractThis thesis has two distinct yet related parts, the first pertaining to geometry on quasi-metric spaces with emphasis on the Hausdorff outer-measure, the natural extension of the Gromov-Pompeiu-Hausdorff distance to quasi-metric spaces, and smoothness of quasi-metric spaces, and the second dealing with Euclidean geometry, namely the role geometry plays in analysis, particularly in the characterization of Lipschitz domains via cones, domains of class C[superscript 1], [superscript w], where w is a modulus of continuity, via pseudo-balls, which includes Lyapunov domains, a sharp version of the Hopf-Oleinik boundary point principle, and subsequently the strong maximum principle.eng
dc.format.extentiv, 309 pageseng
dc.identifier.urihttp://hdl.handle.net/10355/11158
dc.languageEnglisheng
dc.publisherUniversity of Missouri--Columbiaeng
dc.relation.ispartofcommunityUniversity of Missouri-Columbia. Graduate School. Theses and Dissertations. Theses. 2011Theseseng
dc.rightsOpenAccess.eng
dc.rights.licenseThis work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License.
dc.subject.lcshQuasi-metric spaceseng
dc.subject.lcshHausdorff measureseng
dc.subject.lcshHausdorff compactificationseng
dc.subject.lcshLipschitz spaceseng
dc.subject.lcshLyapunov functionseng
dc.subject.lcshH-functionseng
dc.titleQuasi-metric geometry : smoothness and convergence resultseng
dc.typeThesiseng
thesis.degree.disciplineMathematics (MU)eng
thesis.degree.grantorUniversity of Missouri--Columbiaeng
thesis.degree.levelMasterseng
thesis.degree.nameM.A.eng


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