{"paper":{"title":"H\\\"older estimates for degenerate complex Monge-Amp\\`ere equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.CV","authors_text":"Bin Guo, Jacob Sturm, Jian Song, Slawomir Kolodziej","submitted_at":"2025-08-28T15:57:49Z","abstract_excerpt":"Uniform $L^\\infty$ and H\\\"older estimates were proved by the Kolodziej for complex Monge-Amp\\`ere equations on compact K\\\"ahler manifolds with $L^p$ volume measure with $p>1$. On the other hand, establishing H\\\"older estimates on singular K\\\"ahler varieties has remained open. In this paper, we establish uniform H\\\"older continuity for a family of complex Monge-Amp\\`ere equations on K\\\"ahler varieties, by developing a geometric regularization based on the partial $C^0$ estimate, i.e., quantitive Kodaira embeddings. As an application, we prove that local potentials of smoothable K\\\"ahler-Einstei"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.20933","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/2508.20933/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"}