Weak convergence of Monge-Amp\`ere measures on compact Hermitian manifolds

Ngoc Cuong Nguyen; Slawomir Kolodziej

Weak convergence of Monge-Amp\`ere measures on compact Hermitian manifolds

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arxiv 2212.11550 v1 pith:O3ZDOQWR submitted 2022-12-22 math.CV

Slawomir Kolodziej , Ngoc Cuong Nguyen This is my paper · ORCID

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keywords monge-ampomegaboundedhermitianmeasuresplurisubharmonicsequenceassociated

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abstract

We give a sufficient condition on a sequence of uniformly bounded $\omega$-plurisubharmonic functions, $\omega$ being a Hermitian metric, for which the sequence of associated Monge-Amp\`ere measures converges weakly. This criterion can be used to obtained a bounded $\omega$-plurisubharmonic solution to the Monge-Amp\`ere equation.

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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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