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Degenerate complex Monge-Amp\`ere equations on some compact Hermitian manifolds

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arxiv 2401.03440 v2 pith:WIGGLMYD submitted 2024-01-07 math.CV

Mohammed Salouf This is my paper · ORCID
classification math.CV
keywords complexmonge-ampcompactdegenerateequationshermitianthetaadmits
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abstract

Let $X$ be a compact complex manifold which admits a hermitian metric satisfying a curvature condition introduced by Guan-Li. Given a semipositive form $\theta$ with positive volume, we define the Monge-Amp\`ere operator for unbounded $\theta$-psh functions and prove that it is continuous with respect to convergence in capacity. We then develop pluripotential tools to study degenerate complex Monge-Amp\`ere equations in this context, extending recent results of Tosatti-Weinkove, Kolodziej-Nguyen, Guedj-Lu and many others who treat bounded solutions.

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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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