{"paper":{"title":"On the modulus of continuity of solutions to complex Monge-Amp\\`ere equations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AP","math.CV"],"primary_cat":"math.DG","authors_text":"Bin Guo, Chuwen Wang, Duong H. Phong, Freid Tong","submitted_at":"2021-12-04T14:59:54Z","abstract_excerpt":"In this paper, we prove a uniform and sharp estimate for the modulus of continuity of solutions to complex Monge-Amp\\`ere equations, using the PDE-based approach developed by the first three authors in their approach to supremum estimates for fully non-linear equations in K\\\"ahler geometry. As an application, we derive a uniform diameter bound for K\\\"ahler metrics satisfying certain Monge-Amp\\`ere equations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.02354","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/2112.02354/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"}