{"paper":{"title":"On the regularity problem of complex Monge-Ampere equations with conical singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Xiuxiong Chen, Yuanqi Wang","submitted_at":"2014-05-05T19:59:18Z","abstract_excerpt":"In the category of metrics with conical singularities along a smooth divisor with angle in $(0, 2\\pi)$, we show that locally defined weak solutions ($C^{1,1}-$solutions) to the K\\\"ahler-Einstein equations actually possess maximum regularity, which means the metrics are actually H\\\"older continuous in the singular polar coordinates. This shows the weak K\\\"ahler-Einstein metrics constructed by Guenancia-Paun \\cite{GP}, and independently by Yao \\cite{GT}, are all actually strong-conical K\\\"ahler-Einstein metrics. The key step is to establish a Liouville-type theorem for weak-conical K\\\"ahler-Ricc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.1021","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":""},"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"}