The cross-curvature flow conjecture for negatively curved three-manifolds
The cross-curvature flow conjecture for negatively curved three-manifolds
Let be a three-manifold equipped with a negatively curved metric, and let the Cross Curvature Flow (XCF) evolve this metric. A hyperbolic metric is a metric of constant negative sectional curvature. Cross-curvature flow conjecture. The XCF deforms arbitrary negatively curved metrics to a hyperbolic metric. This conjecture would extend the preceding result from integrable negatively curved metrics to arbitrary negatively curved metrics. The source does not state that it has been resolved.
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Primary source
Paul Bryan, Mohammad N. Ivaki and Julian Scheuer, “Negatively Curved Three-Manifolds, Hyperbolic Metrics, Isometric Embeddings In Minkowski Space And The Cross Curvature Flow”, arXiv:1906.02381 (2019).
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