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Title: Instantaneously complete Ricci flows on surfaces
Author: Giesen, Gregor
ISNI:       0000 0004 2726 0988
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 2012
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The intention of this thesis is to give a survey of instantaneously complete Ricci flows on surfaces, focussing on the existence and uniqueness of its Cauchy problem. We prove a general existence result for instantaneously complete Ricci flows starting at an arbitrary Riemannian surface which may be incomplete and may have unbounded curvature. We give an explicit formula for the maximal existence time, and describe the asymptotic behaviour in most cases. The issue of uniqueness within this class of instantaneously complete Ricci flows is still conjectured but we are going to describe the progress towards its proof. Finally, we apply that new existence result in order to construct an immortal complete Ricci flow which has unbounded curvature for all time.
Supervisor: Not available Sponsor: Leverhulme Trust (LT)
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics