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Ricci flow on asymptotically conical surfaces with nontrivial topology
-
James Isenberg
,
Rafe Mazzeo
Published/Copyright:
January 21, 2012
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.
Received: 2010-05-25
Revised: 2011-04-15
Published Online: 2012-01-21
Published in Print: 2013-03
©[2013] by Walter de Gruyter Berlin Boston
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Articles in the same Issue
- Conjecture de type de Serre et formes compagnons pour GSp4
- Extension of plurisubharmonic functions with growth control
- Additivity and non-additivity for perverse signatures
- MacMahon's sum-of-divisors functions, Chebyshev polynomials, and quasi-modular forms
- The prime geodesic theorem
- Inequities in the Shanks–Rényi prime number race: An asymptotic formula for the densities
- Klein approximation and Hilbertian fields
- Ricci flow on asymptotically conical surfaces with nontrivial topology
