%0 Journal Article
%T Ricci flow on asymptotically conical surfaces with nontrivial topology
%A James Isenberg
%A Rafe Mazzeo
%A Natasa Sesum
%J Mathematics
%D 2010
%I arXiv
%X 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 $t^{-1}g(t)$ 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 $g_0$.
%U http://arxiv.org/abs/1003.5237v1