Stability of hyperbolic space under Ricci flow

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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} }

Simon, Miles We study the Ricci flow of initial metrics which are C<sup>0</sup>-perturbations of the hyperbolic metric on H<sup>n</sup>[Hyperbolic n-space]. If the perturbation is bounded in the L<sup>2</sup>-sense, and small enough in the C<sup>0</sup>-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<sup>k</sup>-norms and in the L<sup>2</sup>-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. Schulze, Felix Schnürer, Oliver Christian eng Publ. in: Communications in analysis and geometry ; 19 (2011), 5. - S. 1023-1047 Simon, Miles terms-of-use Schulze, Felix Schnürer, Oliver Christian Stability of hyperbolic space under Ricci flow 2012-06-13T10:54:11Z 2012-06-13T10:54:11Z 2011

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