Ricci flow on asymptotically conical surfaces with nontrivial topology

2010/03/26 by James Isenberg, Rafe Mazzeo, Isenberg, James +3 · 1 citation
Mathematics · #53C44 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53C44

paper · pdf · doi:10.48550/arxiv.1003.5237

arxiv created 2010/03/26 · arxiv updated 2010/03/30

Abstract

As part of the general investigation of Ricci flow on complete surfaces with finite total curvature, we study this flow for surfaces with asymptotically conical (which includes as a special case asymptotically Euclidean) geometries. After establishing long-time existence, and in particular the fact that the flow preserves the asymptotically conic geometry, we prove that the solution metric g(t) expands at a locally uniform linear rate; moreover, the rescaled family of metrics t^-1g(t) exhibits a transition at infinite time inasmuch as it converges locally uniformly to a complete, finite area hyperbolic metric which is the unique uniformizing metric in the conformal class of the initial metric g₀.

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