High Energy plurisubharmonic classes
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914101035270144 |
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| author | Guedj, Vincent Zeriahi, Ahmed |
| author_facet | Guedj, Vincent Zeriahi, Ahmed |
| contents | Let $Ω\Subset \C^n$ be a bounded strongly pseudoconvex domain. For any concave increasing weight $χ: \R^- \longrightarrow \R^-$ such that $χ(0) = 0$, we introduce and study finite energy classes $\mathcal E_χ(Ω)$ of plurisubharmonic functions, using the Orlicz space formalism. We investigate the range of the Monge-Ampère operator on these classes, and conjecture that this should lead to an integral characterization of the image of bounded plurisubharmonic functions, an open problem since the birth of Pluripotential Theory more than forty years ago. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_16412 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | High Energy plurisubharmonic classes Guedj, Vincent Zeriahi, Ahmed Complex Variables Analysis of PDEs Let $Ω\Subset \C^n$ be a bounded strongly pseudoconvex domain. For any concave increasing weight $χ: \R^- \longrightarrow \R^-$ such that $χ(0) = 0$, we introduce and study finite energy classes $\mathcal E_χ(Ω)$ of plurisubharmonic functions, using the Orlicz space formalism. We investigate the range of the Monge-Ampère operator on these classes, and conjecture that this should lead to an integral characterization of the image of bounded plurisubharmonic functions, an open problem since the birth of Pluripotential Theory more than forty years ago. |
| title | High Energy plurisubharmonic classes |
| topic | Complex Variables Analysis of PDEs |
| url | https://arxiv.org/abs/2510.16412 |