Asymptotic Stability of the Cross Curvature Flow at a Hyperbolic Metric

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.

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

References in corpus (1)

• Cross Curvature Flow on Locally Homogenous Three-manifolds (I)

Cited by in corpus (1)

• The second variation of the Ricci expander entropy