Asymptotics and convergence for the complex Monge-Ampere equation

2018/06/14 by Han, Qing, Jiang, Xumin
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1806.05371

Abstract

We study the asymptotics of complete Kaehler-Einstein metrics on strictly pseudoconvex domains in Cⁿ and derive a convergence theorem for solutions to the corresponding Monge-Ampere equation. If only a portion of the boundary is analytic, the solutions satisfy Gevrey type estimates for tangential derivatives. A counterexample for the model linearized equation suggests that there is no local convergence theorem for the complex Monge-Ampere equation

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