Asymptotic Stability of the Cross Curvature Flow at a Hyperbolic Metric
Abstract
Description
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.
Revised version including additional references and enhanced exposition. To appear in PAMS
Revised version including additional references and enhanced exposition. To appear in PAMS