Dirichlet problem of complex Monge-Amp\`ere equation near an isolated KLT singularity
Abstract
We solve the Dirichlet Problem of Monge-Amp\`ere equation near an isolate Klt singularity, which generalizes the result of Eyssidieux-Guedj-Zeriahi EGZ, where the Monge-Amp\`ere equation is solved on singular varieties without boundary. As a corollary, we construct solutions to Monge-Amp\`ere equation with isolated singularity on strongly pseudoconvex domain contained in Cn.
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