Publikation: Stability of hyperbolic space under Ricci flow
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2010
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Zusammenfassung
We study the Ricci flow of initial metrics which are C^0-perturbations of the hyperbolic metric on H^n. If the perturbation is bounded in the L^2-sense, and small enough in the C^0-sense, then we show the following: In dimensions four and higher, the scaled Ricci harmonic map heat flow of such a metric converges smoothly, uniformly and exponentially fast in all C^k-norms and in the L^2-norm to the hyperbolic metric as time approaches infinity. We also prove a related result for the Ricci flow and for the two-dimensional conformal Ricci flow.
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Fachgebiet (DDC)
510 Mathematik
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Ricci flow, stability, hyperbolic space
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SCHNÜRER, Oliver C., Felix SCHULZE, Miles SIMON, 2010. Stability of hyperbolic space under Ricci flowBibTex
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year={2010},
series={Konstanzer Schriften in Mathematik},
title={Stability of hyperbolic space under Ricci flow},
number={270},
author={Schnürer, Oliver C. and Schulze, Felix and Simon, Miles}
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<dcterms:abstract xml:lang="eng">We study the Ricci flow of initial metrics which are C^0-perturbations of the hyperbolic metric on H^n. If the perturbation is bounded in the L^2-sense, and small enough in the C^0-sense, then we show the following: In dimensions four and higher, the scaled Ricci harmonic map heat flow of such a metric converges smoothly, uniformly and exponentially fast in all C^k-norms and in the L^2-norm to the hyperbolic metric as time approaches infinity. We also prove a related result for the Ricci flow and for the two-dimensional conformal Ricci flow.</dcterms:abstract>
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