Degenerate complex Monge-Ampère equations on some compact Hermitian manifolds

2024/01/07 by Mohammed Salouf, Salouf, Mohammed · 2 citations
Mathematics · #Geometry and complex manifolds #Geometric Analysis and Curvature Flows #Algebraic Geometry and Number Theory

paper · pdf · doi:10.48550/arxiv.2401.03440

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 θ with positive volume, we define the Monge-Ampère operator for unbounded θ-psh functions and prove that it is continuous with respect to convergence in capacity. We then develop pluripotential tools to study degenerate complex Monge-Ampère 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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• Mixed Hessian inequalities on Hermitian manifolds and applications
• Monge-Ampère equations with prescribed singularities on compact Hermitian manifolds

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