{"paper":{"title":"Weak convergence of complex Monge-Amp\\`ere operators on compact Hermitian manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Haoyuan Sun, Kai Pang, Zhiwei Wang","submitted_at":"2024-12-16T08:27:57Z","abstract_excerpt":"Let $(X,\\omega)$ be a compact Hermitian manifold and let $\\{\\beta\\}\\in H^{1,1}(X,\\mathbb R)$ be a real $(1,1)$-class with a smooth representative $\\beta$, such that $\\int_X\\beta^n>0$. Assume that there is a bounded $\\beta$-plurisubharmonic function $\\rho$ on $X$. First, we provide a criterion for the weak convergence of non-pluripolar complex Monge-Amp\\`ere measures associated to a sequence of $\\beta$-plurisubharmonic functions. Second, this criterion is utilized to solve a degenerate complex Monge-Amp\\`ere equation with an $L^1$-density. Finally, an $L^\\infty$-estimate of the solution to the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.11547","kind":"arxiv","version":1},"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/2412.11547/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"}