Extrema of curvature functional on the space of metrics on 3-manifolds

DOI10.1007/s005260050066zbMath0889.58027OpenAlexW2079651583MaRDI QIDQ1357760

Michael T. Anderson

Publication date: 8 June 1998

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s005260050066

zbMATH Keywords

convergencecurvature functionalcritical metricsThurston geometrization conjectureYamabe metrics

Mathematics Subject Classification ID

Global Riemannian geometry, including pinching (53C20) Critical metrics (58E11) Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) (58J60)

Related Items (19)

Scalar curvature and the existence of geometric structures on 3-manifolds, I ⋮ Critical metrics of the $L^{2}$-norm of the scalar curvature ⋮ Rigidity of Einstein metrics as critical points of quadratic curvature functionals on closed manifolds ⋮ Rigidity of critical metrics for quadratic curvature functions on closed Riemannian manifolds ⋮ Some rigidity results on critical metrics for quadratic functionals ⋮ Some characterizations on critical metrics for quadratic curvature functions ⋮ Critical metrics of the Schouten functional ⋮ Rigidity of critical metrics for quadratic curvature functionals ⋮ The ground state and the long-time evolution in the CMC Einstein flow ⋮ Boundary regularity, uniqueness and non-uniqueness for AH Einstein metrics on 4-manifolds. ⋮ Maximum solutions of normalized Ricci flow on 4-manifolds ⋮ On the stability of the \(L^p\)-norm of the Riemannian curvature tensor ⋮ Scalar curvature and the existence of geometric structures on 3-manifolds, II ⋮ Some rigidity characterizations on critical metrics for quadratic curvature functionals ⋮ Some rigidity characterizations of Einstein metrics as critical points for quadratic curvature functionals ⋮ Improved breakdown criterion for einstein vacuum equations in CMC gauge ⋮ Recent developments on the Ricci flow ⋮ On conformally flat critical Riemannian metrics for a curvature functional ⋮ On critical Riemannian metrics for a curvature functional on 3-manifolds

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