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arXiv · 0906.4592

Cross curvature flow on a negatively curved solid torus

Jason DeBlois·Dan Knopf·Andrea Young
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Abstract

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.

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Jason DeBlois, Dan Knopf, Andrea Young. 2009-06-25. Cross curvature flow on a negatively curved solid torus. https://doi.org/10.2140/agt.2010.10.343

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