Asymptotic Stability of the Cross Curvature Flow at a Hyperbolic Metric
Differential Geometry
2008-02-06 v2
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.
Keywords
Cite
@article{arxiv.math/0609767,
title = {Asymptotic Stability of the Cross Curvature Flow at a Hyperbolic Metric},
author = {Dan Knopf and Andrea Young},
journal= {arXiv preprint arXiv:math/0609767},
year = {2008}
}
Comments
Revised version including additional references and enhanced exposition. To appear in PAMS