Dirichlet problem of complex Monge-Ampère equation near an isolated KLT singularity

Abstract

We solve the Dirichlet Problem of Monge-Ampère equation near an isolate Klt singularity, which generalizes the result of Eyssidieux-Guedj-Zeriahi [10], 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 Ω contained in C n .