Volume 19, issue 3 (2015)

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Uniqueness of instantaneously complete Ricci flows

Peter M Topping

Geometry & Topology 19 (2015) 1477–1492

We prove uniqueness of instantaneously complete Ricci flows on surfaces. We do not require any bounds of any form on the curvature or its growth at infinity, nor on the metric or its growth (other than that implied by instantaneous completeness). Coupled with earlier work, this completes the well-posedness theory for instantaneously complete Ricci flows on surfaces.

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Ricci flow, logarithmic fast diffusion equation
Mathematical Subject Classification 2010
Primary: 35K55, 53C44
Secondary: 58J35
Received: 23 December 2013
Accepted: 22 August 2014
Published: 21 May 2015
Proposed: Tobias H Colding
Seconded: Bruce Kleiner, Colin Rourke
Peter M Topping
Mathematics Institute
University of Warwick
Coventry CV4 7AL