{"paper":{"title":"Schauder estimates for equations with cone metrics, I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Bin Guo, Jian Song","submitted_at":"2016-11-30T23:19:38Z","abstract_excerpt":"This is the first paper in a series to develop a linear and nonlinear theory for elliptic and parabolic equations on K\\\"ahler varieties with mild singularities. Donaldson has established a Schauder estimate for linear and complex Monge-Amp\\`ere equations when the background K\\\"ahler metrics on $\\mathbb{C}^n$ have cone singularities along a smooth complex hypersurface. We prove a sharp pointwise Schauder estimate for linear elliptic and parabolic equations on $\\mathbb{C}^n$ with background metric $g_\\beta= \\sqrt{-1} ( dz_1 \\wedge d\\bar{z_1} + \\ldots + \\beta^2|z_n|^{-2(1-\\beta)} dz_n \\wedge d\\ba"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.00075","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"}