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

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dc.creatorChow, Bennett
dc.creatorHamilton, Richard
dc.date2003-08-31
dc.date.accessioned2026-07-07T05:00:43Z
dc.date.available2026-07-07T05:00:43Z
dc.descriptionWe introduce a geometric evolution equation for 3-manifolds with sectional curvature of one sign which is in some sense dual to the Ricci flow. On a closed 3-manifold with negative sectional curvature, we establish short time existence and a pair of monotonicity formulas for solutions to the flow. One of these formulas shows that, provided the solution exists for all time, the metric approaches hyperbolic in an integral sense. Long time existence is still an open problem.
dc.description6 pages, submitted to the Proceedings of the 10th Gokova Geometry Topology Conference, May 26-31, 2003, Gokova, Turkey
dc.identifierhttps://arxiv.org/abs/math/0309008
dc.identifierhttp://arxiv.org/abs/math/0309008
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/68425
dc.subjectDifferential Geometry
dc.subjectGeometric Topology
dc.subject53C44
dc.titleThe Cross Curvature Flow of 3-manifolds with Negative Sectional Curvature
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