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Ricci flow and metric Geometry
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Coffey, Michael R. (2015) Ricci flow and metric Geometry. PhD thesis, University of Warwick.
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WRAP_THESIS_Coffey_2015.pdf - Submitted Version - Requires a PDF viewer. Download (1035Kb) | Preview |
Official URL: http://webcat.warwick.ac.uk/record=b2762178~S1
Abstract
This thesis considers two separate problems in the field of Ricci flow on surfaces. Firstly, we examine the situation of the Ricci flow on Alexandrov surfaces, which are a class of metric spaces equipped with a notion of curvature. We extend the existence and uniqueness results of Thomas Richard in the closed case to the setting of non-compact Alexandrov surfaces that are uniformly non-collapsed. We complement these results with an extensive survey that collects together, for the first time, the essential topics in the metric geometry of Alexandrov spaces due to a variety of authors.
Secondly, we consider a problem in the well-posedness theory of the Ricci flow on surfaces. We show that given an appropriate initial Riemannian surface, we may construct a smooth, complete, immortal Ricci flow that takes on the initial surface in a geometric sense, in contrast to the traditional analytic notions of initial condition. In this way, we challenge the contemporary understanding of well-posedness for geometric equations.
Item Type: | Thesis (PhD) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Ricci flow, Geometry, Riemannian | ||||
Official Date: | April 2015 | ||||
Dates: |
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Institution: | University of Warwick | ||||
Theses Department: | Mathematics Institute | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Topping, Peter, 1971- | ||||
Extent: | vi, 94 leaves | ||||
Language: | eng |
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