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The natural objects one has to consider in order to explore the differential-geometric properties of the pair $(X, D)$ are the so-called metrics with conic singularities. In this article, we complete our earlier work \\cite{CGP} concerning the Monge-Amp\\`ere equations on $(X, D)$ by establishing Laplacian and ${\\mathscr C}^{2,\\alpha, \\beta}$ estimates for the solution of this equations regardless to the size o"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1307.6375","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-07-24T10:43:30Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"d36934e45341096b2a634b78bb5f08e45a6015e1a151b649373ac3445830f19f","abstract_canon_sha256":"0577c710030d8ad02179f74aeabf238a5c9034cc5b3061a816829db29173a8d7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:24.289276Z","signature_b64":"QQyMGYfR1n1baDlsIhWV4fZsG3zSS54h9kqhLzInnX2xuD+Suor2fay2/vhiYkwMblnCSSRvGX/gVfNhyNUqAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cff8a3cf37b87f135c12910a34833408f7c51559c8e9b9380e391a4f4bb9cabc","last_reissued_at":"2026-05-18T01:15:24.288648Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:24.288648Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Conic singularities metrics with prescribed Ricci curvature: the case of general cone angles along normal crossing divisors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DG","authors_text":"Henri Guenancia, Mihai P\\u{a}un","submitted_at":"2013-07-24T10:43:30Z","abstract_excerpt":"Let $X$ be a non-singular compact K\\\"ahler manifold, endowed with an effective divisor $D= \\sum (1-\\beta_k) Y_k$ having simple normal crossing support, and satisfying $\\beta_k \\in (0,1)$. 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