Turkish Journal of Mathematics
We consider the cross curvature flow, an evolution equation of metrics on 3-manifolds. We establish short time existence when the sectional curvature has a sign. In the case of negative sectional curvature, we obtain some monotonicity formulas which support the conjecture that after normalization, for initial metrics on closed 3-manifolds with negative sectional curvature, the solution exists for all time and converges to a hyperbolic metric. This conjecture is still open at the present time.
Cross curvature flow, geometric evolution equation, negative sectional curvature, monotonicity formula, hyperbolic metric
CHOW, BENNETT and HAMILTON, RICHARD S. (2004) "The Cross Curvature Flow of 3-Manifolds with Negative Sectional Curvature," Turkish Journal of Mathematics: Vol. 28: No. 1, Article 1. Available at: https://journals.tubitak.gov.tr/math/vol28/iss1/1