Abstract
The classic –Theorem of Gromov and Thurston constructs a negatively curved metric on certain –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 “–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.
Citation
Jason DeBlois. Dan Knopf. Andrea Young. "Cross curvature flow on a negatively curved solid torus." Algebr. Geom. Topol. 10 (1) 343 - 372, 2010. https://doi.org/10.2140/agt.2010.10.343
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