Dirichlet problem for complex Monge–Ampère equation near an isolated KLT singularity

Abstract

We solve the Dirichlet problem for complex Monge–Ampère equation near an isolate Klt singularity, which generalizes the result of Eyssidieux et al. [Singular Kähler–Einstein metrics, J. Amer. Math. Soc. 22 (2009) 607–639], where the Monge–Ampère equation is solved on singular varieties without boundary. As a corollary, we construct solutions to Monge–Ampère equation with isolated singularity on strongly pseudoconvex domain [Formula: see text] contained in [Formula: see text].