{"paper":{"title":"Conformal metrics with constant curvature one and finite conical singularities on compact Riemann surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.DG","authors_text":"Bin Xu, Qing Chen, Wei Wang, Yingyi Wu","submitted_at":"2013-02-26T20:53:43Z","abstract_excerpt":"A conformal metric $g$ with constant curvature one and finite conical singularities on a compact Riemann surface $\\Sigma$ can be thought of as the pullback of the standard metric on the 2-sphere by a multi-valued locally univalent meromorphic function $f$ on $\\Sigma\\backslash \\{{\\rm singularities}\\}$, called the {\\it developing map} of the metric $g$. When the developing map $f$ of such a metric $g$ on the compact Riemann surface $\\Sigma$ has reducible monodromy, we show that, up to some M{\\\" o}bius transformation on $f$, the logarithmic differential $d\\,(\\log\\, f)$ of $f$ turns out to be an a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.6457","kind":"arxiv","version":2},"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"}