{"paper":{"title":"Degenerate complex Monge-Amp\\`ere equations with non-K\\\"ahler forms in bounded domains","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Mohammed Salouf","submitted_at":"2023-03-08T21:29:43Z","abstract_excerpt":"In this paper, we study weak solutions to complex Monge-Amp\\`ere equations of the form $(\\omega + dd^c \\varphi)^n= F(\\varphi,.)d\\mu$ on a bounded strictly pseudoconvex domain in $\\mathbb{C}^n$, where $\\omega$ is a smooth $(1,1)$-form, $0\\leq F$ is a continuous non-decreasing function, and $\\mu$ is a positive non-pluripolar measure. Our results extend previous works of Ko{\\l}odziej and Nguyen \\cite{KN15,KN23a,KN23b} who study bounded solutions, as well as Cegrell \\cite{Ceg98,Ceg04,Ceg08}, Czy\\.z \\cite{Cz09}, Benelkourchi \\cite{Ben09,Ben15} and others who treat the case when $\\omega=0$ and/or $F"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.04897","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2303.04897/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}