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 \cite{EGZ}, 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 $\hat{I}\text{c◯}$ contained in ${\mathbb{C}}^n$.

Minor change from V1. arXiv admin note: text overlap with arXiv:2106.05486