{"paper":{"title":"A $\\mathcal C^{2,\\alpha}$ estimate of the complex Monge-Amp\\`ere equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Chao Li, Jiayu Li, Xi Zhang","submitted_at":"2017-05-24T07:09:05Z","abstract_excerpt":"In this paper, we prove a $\\mathcal C^{2,\\alpha}$-estimate for the solution to the complex Monge-Amp\\`ere equation $\\det(u_{i\\bar{j}})=f$ with $0< f\\in \\mathcal C^{\\alpha}$, under the assumption that $u\\in \\mathcal C^{1,\\beta }$ for some $\\beta <1$ which depends on $n$ and $\\alpha $."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.08634","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"}