{"paper":{"title":"Quasi-plurisubharmonic envelopes 1: Uniform estimates on K\\\"ahler manifolds","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.CV","authors_text":"Chinh H. Lu, Vincent Guedj","submitted_at":"2021-06-08T12:07:30Z","abstract_excerpt":"We develop a new approach to $L^{\\infty}$-a priori estimates for degenerate complex Monge-Amp\\`ere equations on complex manifolds. It only relies on compactness and envelopes properties of quasi-plurisubharmonic functions. Our method allows one to obtain new and efficient proofs of several fundamental results in K\\\"ahler geometry as we explain in this article. In a sequel we shall explain how this approach also applies to the hermitian setting producing new relative a priori bounds, as well as existence results."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.04273","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/2106.04273/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"}