Asymptotic stability of the cross curvature flow at a hyperbolic metric

DOI10.1090/S0002-9939-08-09534-8zbMath1168.53034arXivmath/0609767OpenAlexW2008435405WikidataQ125802201 ScholiaQ125802201MaRDI QIDQ3605027

Andrea Young, Dan Knopf

Publication date: 25 February 2009

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0609767

zbMATH Keywords

asymptotic stabilityRicci flow.hyperbolization conjecturecross curvature flownegatively curved three-manifolds

Mathematics Subject Classification ID

Related Items (7)

Unnamed Item ⋮ Generalized cross curvature flow ⋮ On the cross curvature flow ⋮ Stability of complex hyperbolic space under curvature-normalized Ricci flow ⋮ Perelman's lambda-functional and the stability of Ricci-flat metrics ⋮ Cross curvature flow on a negatively curved solid torus ⋮ Convergence stability for Ricci flow

Cites Work

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• On the topology of the space of negatively curved metrics
• On the second derivative of the total scalar curvature
• Cross curvature flow on locally homogeneous three-manifolds. I.
• Pinching constants for hyperbolic manifolds
• Stability of the Ricci flow at Ricci-flat metrics
• A caveat on the convergence of the Ricci flow for pinched negatively curved manifolds
• Examples for cross curvature flow on 3-manifolds
• Ricci Flow, Einstein Metrics and Space Forms
• Short-time existence of solutions to the cross curvature flow on 3-manifolds
• Riemannian Groupoids and Solitons for Three-Dimensional Homogeneous Ricci and Cross-Curvature Flows
• Analytic semigroups and optimal regularity in parabolic problems

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