%0 Journal Article
%T Cross curvature flow on a negatively curved solid torus
%A Jason DeBlois
%A Dan Knopf
%A Andrea Young
%J Mathematics
%D 2009
%I arXiv
%R 10.2140/agt.2010.10.343
%X The classic 2pi-Theorem of Gromov and Thurston constructs a negatively curved metric on certain 3-manifolds obtained by Dehn filling. By Geometrization, any such manifold admits a hyperbolic metric. We outline a program using cross curvature flow to construct a smooth one-parameter family of metrics between the "2pi-metric" and the hyperbolic metric. We make partial progress in the program, proving long-time existence, preservation of negative sectional curvature, curvature bounds, and integral convergence to hyperbolic for the metrics under consideration.
%U http://arxiv.org/abs/0906.4592v1