Regularity of the geodesic equation in the space of Sasakian metrics

DOI10.1016/j.aim.2011.12.002zbMath1245.58016arXiv0906.5591OpenAlexW2010965113MaRDI QIDQ411735

Xi Zhang, Pengfei Guan

Publication date: 30 April 2012

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0906.5591

zbMATH Keywords

Sasakian manifoldconstant scalar curvaturegeodesic equationdegenerate complex Monge-Ampère equation

Mathematics Subject Classification ID

Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) (58J60) Complex Monge-Ampère operators (32W20) Manifolds of metrics (especially Riemannian) (58D17)

Related Items (12)

Higgs bundles over foliation manifolds ⋮ On the \(J\)-flow in Sasakian manifolds ⋮ Uniqueness of constant scalar curvature Sasakian metrics ⋮ On the convergence of the Sasaki \(J\)-flow ⋮ Geometric pluripotential theory on Sasaki manifolds ⋮ Curvature of the completion of the space of Sasaki potentials ⋮ Fully nonlinear elliptic equations for conformal deformations of Chern-Ricci forms ⋮ \(C^{1,1}\) regularity of degenerate complex Monge-Ampère equations and some applications ⋮ Unnamed Item ⋮ On the Dirichlet problem for fully nonlinear elliptic equations on annuli of metric cones ⋮ A fully nonlinear partial differential equation and its application to the \(\sigma_k\)-Yamabe problem ⋮ On the Dirichlet problem for a class of fully nonlinear elliptic equations

Cites Work

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• Einstein metrics on spheres
• Toric geometry, Sasaki-Einstein manifolds and a new infinite class of AdS/CFT duals
• Sasaki-Einstein manifolds and volume minimisation
• Uniqueness and examples of compact toric Sasaki-Einstein metrics
• Space of Kähler metrics. III: On the lower bound of the Calabi energy and geodesic distance
• A gradient estimate in the Calabi-Yau theorem
• Geometry of Kähler metrics and foliations by holomorphic discs
• K-energy maps integrating Futaki invariants
• Some symplectic geometry on compact Kähler manifolds. I
• The Dirichlet problem for complex Monge-Ampère equations and regularity of the pluri-complex Green function
• A nonlinear elliptic system for maps from Hermitian to Riemannian manifolds and rigidity theorems in Hermitian geometry
• Boundary-value problems on \(S^ n\) for surfaces of constant Gauss curvature
• The space of Kähler metrics.
• Uniqueness of Sasaki-Einstein metrics
• The space of Kähler metrics. II.
• The extremal function associated to intrinsic norms.
• Partial differential equations. 1: Basic theory
• Transverse Kähler geometry of Sasaki manifolds and toric Sasaki-Einstein manifolds
• Test configurations for \(k\)-stability and geodesic rays
• The theory of superstring with flux on non-Kähler manifolds and the complex Monge-Ampère equation
• The Monge-Ampère operator and geodesics in the space of Kähler potentials
• On differentiable manifolds with certain structures which are closely related to almost contact structure. I
• Locally Sasakian manifolds
• On the Calabi flow
• THE SASAKI–RICCI FLOW
• The dirichlet problem for nonlinear second-order elliptic equations. II. Complex monge-ampère, and uniformaly elliptic, equations
• Complex Monge-Ampere and Symplectic Manifolds
• Boundary value problems for surfaces of constant Gauss Curvature
• On the ricci curvature of a compact kähler manifold and the complex monge-ampére equation, I

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