{"paper":{"title":"Monge-Amp\\`ere type equation on compact Hermitian manifolds","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DG","authors_text":"Genglong Lin, Xiangyu Zhou, Yinji Li","submitted_at":"2023-11-25T08:01:52Z","abstract_excerpt":"Given a cohomology $(1,1)$-class $\\{\\beta\\}$ of compact Hermitian manifold $(X,\\omega)$ possessing a bounded potential and fixed a model potential $\\phi$, motivated by Darvas-Di Nezza-Lu and Li-Wang-Zhou's work, we show that degenerate complex Monge-Amp\\`ere equation $(\\beta+dd^c \\varphi)^n=e^{\\lambda \\varphi}\\mu$ has a unique solution in the relative full mass class $\\mathcal{E}(X,\\beta,\\phi)$, where $\\mu$ is a non-pluripolar measure on $X$ and $\\lambda\\geq0$ is a fixed constant.\n  As an application, we give an explicit description of Lelong numbers of elements in $\\mathcal{E}(X,\\beta,\\phi)$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.14958","kind":"arxiv","version":3},"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/2311.14958/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"}