The Range of the Monge-Ampère operator $(ω+ dd^c .)^n$ in bounded domains
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915520158105600 |
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| author | Alehyane, Omar Assila, Fatima Zahra Salouf, Mohammed |
| author_facet | Alehyane, Omar Assila, Fatima Zahra Salouf, Mohammed |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_23944 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Range of the Monge-Ampère operator $(ω+ dd^c .)^n$ in bounded domains Alehyane, Omar Assila, Fatima Zahra Salouf, Mohammed Complex Variables 32W20, 32U05, 32Q15, 35A23 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. |
| title | The Range of the Monge-Ampère operator $(ω+ dd^c .)^n$ in bounded domains |
| topic | Complex Variables 32W20, 32U05, 32Q15, 35A23 |
| url | https://arxiv.org/abs/2509.23944 |