Asymptotic Stability of the Cross Curvature Flow at a Hyperbolic Metric

Dan Knopf; Andrea Young

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Asymptotic Stability of the Cross Curvature Flow at a Hyperbolic Metric

Dan Knopf·Andrea Young

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Abstract

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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Dan Knopf, Andrea Young. 2008-02-05. Asymptotic Stability of the Cross Curvature Flow at a Hyperbolic Metric. https://arxiv.org/abs/math/0609767

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