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Title: Ricci flow and metric geometry
Author: Coffey, Michael R.
ISNI:       0000 0004 5348 3456
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 2015
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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.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics