## Algebraic & Geometric Topology

### Cross curvature flow on a negatively curved solid torus

#### Abstract

The classic $2π$–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 “$2π$–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.

#### Article information

Source
Algebr. Geom. Topol., Volume 10, Number 1 (2010), 343-372.

Dates
Revised: 25 November 2009
Accepted: 17 December 2009
First available in Project Euclid: 21 December 2017

https://projecteuclid.org/euclid.agt/1513882316

Digital Object Identifier
doi:10.2140/agt.2010.10.343

Mathematical Reviews number (MathSciNet)
MR2602839

Zentralblatt MATH identifier
1211.53083

#### Citation

DeBlois, Jason; Knopf, Dan; Young, Andrea. Cross curvature flow on a negatively curved solid torus. Algebr. Geom. Topol. 10 (2010), no. 1, 343--372. doi:10.2140/agt.2010.10.343. https://projecteuclid.org/euclid.agt/1513882316

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