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

Authors: WEIHUNG LIAO

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

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