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arXiv · 1003.2107

Stability of hyperbolic space under Ricci flow

Oliver C. Schnürer·Felix Schulze·Miles Simon
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Abstract

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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Oliver C. Schnürer, Felix Schulze, Miles Simon. 2010-03-10. Stability of hyperbolic space under Ricci flow. https://arxiv.org/abs/1003.2107

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