arxivmath (![[info]](http://l-stat.livejournal.com/img/userinfo.gif){kind=small} arxivmath) wrote,@ 2009-06-27 05:41:00 |
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Cross curvature flow on a negatively curved solid torus. (arXiv:0906.4592v1 [math.DG])
Cross curvature flow on a negatively curved solid torus. (arXiv:0906.4592v1 [math.DG])
read more at math updates on arXiv.org
Cross curvature flow on a negatively curved solid torus. (arXiv:0906.4592v1 [math.DG])
Authors: Jason DeBlois, Dan Knopf, Andrea Young
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.
read more at math updates on arXiv.org
