{"paper":{"title":"Uniformization of higher genus finite type log-Riemann surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.CV","authors_text":"Kingshook Biswas, Ricardo Perez-Marco","submitted_at":"2013-05-10T13:44:06Z","abstract_excerpt":"We consider a log-Riemann surface $\\mathcal{S}$ with a finite number of ramification points and finitely generated fundamental group. The log-Riemann surface is equipped with a local holomorphic difffeomorphism $\\pi : \\mathcal{S} \\to \\C$. We prove that $\\mathcal{S}$ is biholomorphic to a compact Riemann surface with finitely many punctures $S$, and the pull-back of the 1-form $d\\pi$ under the biholomorphic map $\\phi : S \\to \\mathcal{S}$ is a 1-form $\\omega = \\phi^* d\\pi$ with isolated singularities at the punctures of exponential type, i.e. near each puncture $p$, $\\omega = e^h \\cdot \\omega_0$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.2339","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"}