The complex Monge-Ampère equation on compact Kähler manifolds

DOI10.1007/s00208-012-0780-6zbMath1253.35070arXiv1004.0543OpenAlexW2156187560MaRDI QIDQ695281

Xiuxiong Chen, Weiyong He

Publication date: 20 December 2012

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1004.0543

Mathematics Subject Classification ID

Existence problems for PDEs: global existence, local existence, non-existence (35A01) Compact Kähler manifolds: generalizations, classification (32J27) Monge-Ampère equations (35J96)

Related Items (12)

Existence of coupled Kähler–Einstein metrics using the continuity method ⋮ Conic singularities metrics with prescribed scalar curvature: a priori estimates for normal crossing divisors ⋮ On \(L^{\infty}\) estimate for complex Hessian quotient equations on compact Kähler manifolds ⋮ Some interior regularity estimates for solutions of complex Monge-Ampère equations on a ball ⋮ On the constant scalar curvature Kähler metrics (I)—A priori estimates ⋮ On the constant scalar curvature Kähler metrics (II)—Existence results ⋮ A \(\mathcal{C}^{2, \alpha}\) estimate of the complex Monge-Ampère equation ⋮ Some new estimates for the complex Monge-Ampère equation ⋮ Coupled Kähler-Ricci solitons on toric Fano manifolds ⋮ Compactness of Kähler metrics with bounds on Ricci curvature and \({\mathcal{I}}\) functional ⋮ On Calabi’s extremal metric and properness ⋮ Local noncollapsing for complex Monge-Ampère equations

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