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arXiv · 2511.02339

Monge-Amp\`ere equations with prescribed singularities on compact Hermitian manifolds

Omar Alehyane·Chinh H. Lu·Mohammed Salouf
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Abstract

Given a compact complex manifold $X$, we study the existence and the uniqueness of weak solutions to degenerate Monge-Amp\`ere equations on $X$ with prescribed singularities when the reference form is semipositive and big, while the right hand side is a non-pluripolar positive Radon measure. This generalizes our previous work to more general hermitian manifolds and also to the case of solutions with prescribed singularities.

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Omar Alehyane, Chinh H. Lu, Mohammed Salouf. 2025-11-04. Monge-Amp\`ere equations with prescribed singularities on compact Hermitian manifolds. https://arxiv.org/abs/2511.02339

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