arXiv subjects

Omar Alehyane

Publications and source records attributed to Omar Alehyane.

2 recordsLinked to original sources

arXiv2025

Monge-Ampère equations with prescribed singularities on compact Hermitian manifolds

Given a compact complex manifold $X$, we study the existence and the uniqueness of weak solutions to degenerate Monge-Ampère 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.

math.CV↗

arXiv2025

The Range of the Monge-Ampère operator $(ω+ dd^c .)^n$ in bounded domains

Let $Ω$ be a bounded strictly pseudoconvex domain of $\mathbb{C}^n$. We solve degenerate complex Monge-Ampère equations of the form $(ω+ dd^c φ)^n = μ$ in the generalized Cegrell classes $\mathcal{K}(Ω,ω,H)$, where $H \in \mathcal{E}(Ω)$ is maximal, $ω$ is a smooth real $(1,1)$-form defined in a neighborhood of $\barΩ$ and $μ$ is a positive Radon measure. This generalizes the previous work of the last author \cite{Sal25} to the case of non-continuous functions $H$ and also to the case of measures $μ$ which do not vanish on pluripolar sets.

math.CV↗