TITLE

The Cross Curvature Flow of 3-Manifolds with Negative Sectional Curvature

AUTHOR(S)
Chow, Bennett; Hamilton, Richard S.
PUB. DATE
March 2004
SOURCE
Turkish Journal of Mathematics;2004, Vol. 28 Issue 1, p1
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
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.
ACCESSION #
13135963

 

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