Asymptotic Stability of the Cross Curvature Flow at a Hyperbolic Metric

Details Asymptotic Stability of the Cross Curvature Flow at a Hyperbolic Metric Asymptotic Stability of the Cross Curvature Flow at a Hyperbolic Metric

2006-09-27

arxiv.org/abs/math/0609767v2

Mathematics

Differential Geometry

Revised version including additional references and enhanced exposition. To appear in PAMS

Scientific paper

We show that there exists a suitable neighborhood of a constant curvature hyperbolic metric such that, for all initial data in this neighborhood, the corresponding solution to a normalized cross curvature flow exists for all time and converges to a hyperbolic metric. We show that the same technique proves an analogous result for Ricci flow. Additionally, we show short time existence and uniqueness of cross curvature flow for a more general class of initial data than was previously known.

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