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At the end of the 19th century Ricci-Curbastro has proved that conversely, every point $x$ of a Ricci surface has a neighborhood which embeds isometrically in $\\mathbb{R}^3$ as a minimal surface, provided $K(x)<0$. We prove this result in full generality by showing that Ricci surfaces can be locally isometrically embedded either minimally in $\\mathbb{R}^3$ or maximally "},"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":"1206.1620","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-06-07T21:16:35Z","cross_cats_sorted":[],"title_canon_sha256":"1b24d99c4c88049ef41ebb8e30145284f9a29f5758c869918655189e1ef68e11","abstract_canon_sha256":"8ad2ff7dac0f28313a805a0aa8a9dfff397bae5c820a5f3d8b4404ce95546f6b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:32.974435Z","signature_b64":"rppFcTpieK5MRuZKy+tbY05I2ZOI3cBHkSrBq7c8wxXpyyP+lytu19sda3bb+6gdISwZ5xfaujJCMJMvS4XoAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fd5be62ab4a052dbfe73af92d120fa9e0b38185f6738ae1dabaef592fbe76a54","last_reissued_at":"2026-05-18T00:52:32.974055Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:32.974055Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ricci surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Andrei Moroianu, Sergiu Moroianu","submitted_at":"2012-06-07T21:16:35Z","abstract_excerpt":"A Ricci surface is a Riemannian 2-manifold $(M,g)$ whose Gaussian curvature $K$ satisfies $K\\Delta K+g(dK,dK)+4K^3=0$. 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