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arXiv · 2401.03440

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

Mohammed Salouf
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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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Mohammed Salouf. 2024-01-07. Degenerate complex Monge-Amp\`ere equations on some compact Hermitian manifolds. https://arxiv.org/abs/2401.03440

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