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

2021/06/18 by Xin Fu, Fu, Xin
Mathematics · #Algebraic Geometry and Number Theory #Analysis of PDEs (math.AP) #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2106.10389

openalex publication_date 2021/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We solve the Dirichlet Problem of Monge-Ampère equation near an isolate Klt singularity, which generalizes the result of Eyssidieux-Guedj-Zeriahi \citeEGZ, 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 ℂⁿ.

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