Giesen, Gregor (2012) Instantaneously complete Ricci flows on surfaces. PhD thesis, University of Warwick.

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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 or Dissertation (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Ricci flow
Date:	June 2012
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Publication Status:	Unpublished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
URI:	http://wrap.warwick.ac.uk/id/eprint/49987

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