Quantitative stability for the complex Monge-Ampere equations

2022/09/01 by Hoang-Son Do, Do, Hoang-Son, Duc‐Viet Vu +1
Mathematics · #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2209.00248

openalex publication_date 2022/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove several quantitative stability estimates for solutions of complex Monge-Ampere equations when both the cohomology class and the prescribed singularity vary. In a broad sense, our results fit well into the study of degeneration of families of Kaehler-Einstein metrics. The key mechanism in our method is the pluripotential theory in the space of potentials of finite lower energy.

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