{"paper":{"title":"Continuity of solutions to complex Monge-Amp\\`{e}re equations on compact K\\\"{a}hler spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.CV"],"primary_cat":"math.DG","authors_text":"Ye-Won Luke Cho, Young-Jun Choi","submitted_at":"2024-01-08T14:51:25Z","abstract_excerpt":"We prove the continuity of bounded solutions to complex Monge-Amp\\`{e}re equations on reduced, locally irreducible compact K\\\"{a}hler spaces. This in particular implies that any singular K\\\"{a}hler-Einstein potentials constructed in \\cite{EGZ09} and \\cite{Tsuji88, TianZhang06, ST17} are continuous. We also provide an affirmative answer to a conjecture in \\cite{EGZ09} by showing that a resolution of any compact normal K\\\"{a}hler space satisfies the continuous approximation property. Finally, we settle the continuity of the potentials of the weak K\\\"{a}hler-Ricci flows \\cite{ST17, GLZ20} on comp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.03935","kind":"arxiv","version":2},"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/2401.03935/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"}