{"paper":{"title":"Asymptotic properties of the hyperbolic metric on the sphere with three conical singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Tanran Zhang","submitted_at":"2013-01-30T16:20:52Z","abstract_excerpt":"The explicit formula for the hyperbolic metric $\\lambda_{\\alpha,\\,\\beta,\\,\\gamma}(z)|dz|$ on the thrice-punctured sphere $\\mathbb{P} \\backslash \\{z_1,\\,z_2,\\,z_3\\}$ with singularities of order $\\alpha,\\,\\beta,\\,\\gamma \\leq 1$ with $\\alpha+\\beta+\\gamma>2$ at $z_1,\\,z_2,\\,z_3$ was given by Kraus, Roth and Sugawa in \\cite{Rothhyper}. In this paper we investigate the asymptotic properties of the higher order derivatives of $\\lambda_{\\alpha,\\,\\beta,\\,\\gamma}(z)$ near the singularity and give some more precise description for the asymptotic behavior."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.7272","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"}