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# Stability of hyperbolic space under Ricci flow

Type of Publication: | Journal article |

Author: | Schnürer, Oliver Christian; Schulze, Felix; Simon, Miles |

Year of publication: | 2011 |

Published in: | Communications in analysis and geometry ; 19 (2011), 5. - pp. 1023-1047 |

DOI (citable link): | https://dx.doi.org/10.4310/CAG.2011.v19.n5.a8 |

Summary: |
We study the Ricci flow of initial metrics which are C
^{0}-perturbations of the hyperbolic metric on H^{n}[Hyperbolic n-space]. 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. |

Subject (DDC): | 510 Mathematics |

Bibliography of Konstanz: | Yes |

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SCHNÜRER, Oliver Christian, Felix SCHULZE, Miles SIMON, 2011. Stability of hyperbolic space under Ricci flow. In: Communications in analysis and geometry. 19(5), pp. 1023-1047. Available under: doi: 10.4310/CAG.2011.v19.n5.a8

@article{Schnurer2011Stabi-19316, title={Stability of hyperbolic space under Ricci flow}, year={2011}, doi={10.4310/CAG.2011.v19.n5.a8}, number={5}, volume={19}, journal={Communications in analysis and geometry}, pages={1023--1047}, author={Schnürer, Oliver Christian and Schulze, Felix and Simon, Miles} }