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Quantitative stability for the complex Monge-Ampere equations

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arxiv 2209.00248 v2 pith:DHBVTPI7 submitted 2022-09-01 math.CV

Hoang-Son Do , Duc-Viet Vu This is my paper · ORCID
classification math.CV
keywords complexequationsmonge-amperequantitativestabilitybroadclasscohomology
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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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  1. Weak convergence of complex Monge-Amp\`ere operators on compact Hermitian manifolds

    math.CV 2024-12 conditional novelty 6.0 of 10

    A weak convergence criterion for non-pluripolar Monge-Ampere measures is proved under only a bounded subsolution, yielding solvability for L1 densities and an L-infinity estimate.

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