Asymptotic stability of the cross curvature flow at a hyperbolic metric

@inproceedings{Knopf2006AsymptoticSO,
  title={Asymptotic stability of the cross curvature flow at a hyperbolic metric},
  author={Dan Knopf and Andrea Young},
  year={2006}
}
We show that for any hyperbolic metric on a closed 3-manifold, there exists a neighborhood such that every solution of a normalized cross curvature flow with initial data in this neighborhood exists for all time and converges to a constant-curvature metric. We demonstrate that the same technique proves an analogous result for Ricci flow. Additionally, we prove short-time existence and uniqueness of cross curvature flow under slightly weaker regularity hypotheses than were previously known. 
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This research was partially supported by an Australian Research Council Discovery grant entitled Geometric evolution equations and global effects of curvature.
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