Quasi-metric geometry: smoothness and convergence results

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Quasi-metric geometry: smoothness and convergence results

Please use this identifier to cite or link to this item: http://hdl.handle.net/10355/11158

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Title: Quasi-metric geometry: smoothness and convergence results
Author: Brigham, Dan, 1987-
Date: 2011
Publisher: University of Missouri--Columbia
Abstract: This 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 C¹, [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.
URI: http://hdl.handle.net/10355/11158
Other Identifiers: BrighamD-050611-T6314

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