Cross curvature flow on a negatively curved solid torus

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.

arXiv comment21 pages

References in corpus (5)

• Ricci flow with surgery on three-manifolds
• Bounds on exceptional Dehn filling
• The shape of hyperbolic Dehn surgery space
• The Cross Curvature Flow of 3-manifolds with Negative Sectional Curvature
• On the topology of the space of negatively curved metrics

Cited by in corpus (2)

• Negatively Curved Three-Manifolds, Hyperbolic Metrics, Isometric Embeddings In Minkowski Space And The Cross Curvature Flow
• Metrics with Prescribed Ricci Curvature near the Boundary of a Manifold