The eternal solution to the cross curvature flow exists in 3-manifolds of negative sectional curvature

Authors : Weihung LIAO

Pages : 2444-2450

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Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :Given a closed 3-manifold $M^3$ endowed with a radial symmetric metric of negative sectional curvature, we define the cross curvature flow on $M^3$; using the maximum principle theorem, we demonstrated that the solution to the cross curvature flow exists for all time and converges pointwise to a hyperbolic metric.
Keywords : Cross curvature flow, geometric evolution equation, negative sectional curvature