Instantaneously complete Ricci flows on surfaces
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
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|
|Institution:||University of Warwick|
|Theses Department:||Mathematics Institute|
|Supervisor(s)/Advisor:||Topping, Peter, 1971-|
|Sponsors:||Leverhulme Trust (LT)|
|Extent:||v, 80 leaves : ill.|
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