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Instantaneously complete Ricci flows on surfaces
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Giesen, Gregor (2012) Instantaneously complete Ricci flows on surfaces. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b2582662~S1
Abstract
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.
Item Type: | Thesis (PhD) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Ricci flow | ||||
Official Date: | June 2012 | ||||
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Publication Status: | Unpublished | ||||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- | ||||
Sponsors: | Leverhulme Trust (LT) | ||||
Extent: | v, 80 leaves : ill. | ||||
Language: | eng |
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