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Long Time Existence of the Cross Curvature Flow in 3-Manifolds with Negative Sectional Curvature

Given a closed 3-manifold with an initial Riemannian metric of negative sec- tional curvature, we consider the cross curvature flow an evolution equation of metric on M3. We prove long-time existence of a solution to the cross curvature flow via the maximum principle theorem. Besides, we demonstrate the solution exists for all time and converges pointwisely to a hyperbolic metric

preprint2016arXivOpen access
Wei-Hung Liao
math.APmath.DG
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Wei-Hung Liao

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