On the Space of Kähler Potentials

DOI10.1002/cpa.21515zbMath1378.53085arXiv1208.1021OpenAlexW2963269388MaRDI QIDQ5498547

Weiyong He

Publication date: 9 February 2015

Published in: Communications on Pure and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1208.1021

zbMATH Keywords

geodesic equationonly mixed second derivatives bounded

Mathematics Subject Classification ID

Global differential geometry of Hermitian and Kählerian manifolds (53C55) Kähler manifolds (32Q15) Manifolds of metrics (especially Riemannian) (58D17)

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The Gursky-Streets equations, Kiselman's principle, the Dirichlet problem for the Monge-Ampère equation, and rooftop obstacle problems, On the Optimal Regularity of Weak Geodesics in the Space of Metrics on a Polarized Manifold, On the \(C^{1,1}\) regularity of geodesics in the space of Kähler metrics, Geometric pluripotential theory on Sasaki manifolds, The Mabuchi geometry of finite energy classes, Geodesic rays and Kähler–Ricci trajectories on Fano manifolds, Geodesic stability, the space of rays and uniform convexity in Mabuchi geometry, C1,1 regularity of geodesics of singular Kähler metrics, Geometric pluripotential theory on Kähler manifolds

Cites Work

• A gradient estimate in the Calabi-Yau theorem
• Some symplectic geometry on compact Kähler manifolds. I
• The Dirichlet problem for a complex Monge-Ampère equation
• The space of Kähler metrics.
• The Space of Volume Forms
• Complex Monge-Ampere and Symplectic Manifolds
• On the ricci curvature of a compact kähler manifold and the complex monge-ampére equation, I
• The complex Monge-Ampère equation and pluripotential theory