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Cross curvature flow on
a negatively curved solid torus
Jason DeBlois, Dan Knopf and Andrea Young |
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Algebraic & Geometric Topology 10 (2010) 343–372
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Abstract |
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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. |
Keywords
cross curvature flow, 2$\pi$–theorem
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Mathematical Subject Classification 2000
Primary: 53C44
Secondary: 57M50, 58J35, 58J32
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References |
Publication
Received: 24 June 2009
Revised: 25 November 2009
Accepted: 17 December 2009
Published: 1 March 2010
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Authors |
| Jason DeBlois | |
| Department of Mathematics,
Statistics and Computer Science University of Illinois at Chicago 322 Science and Engineering Offices (M/C 249) 851 S Morgan Street Chicago, IL 60607-7045 USA |
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| http://www.math.uic.edu/~jdeblois/ | |
| Dan Knopf | |
| Department of Mathematics University of Texas at Austin 1 University Station C1200 Austin, TX 78712-0257 USA |
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| http://www.ma.utexas.edu/users/danknopf | |
| Andrea Young | |
| Department of Mathematics University of Arizona 617 N Santa Rita Ave PO Box 210089 Tucson, AZ 85721-0089 USA |
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| http://math.arizona.edu/~ayoung | |
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