{"paper":{"title":"A Model of the Teichm\\\"uller space of genus-zero bordered surfaces by period maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"David Radnell, Eric Schippers, Wolfgang Staubach","submitted_at":"2017-10-18T23:31:45Z","abstract_excerpt":"We consider Riemann surfaces $\\Sigma$ with $n$ borders homeomorphic to $\\mathbb{S}^1$ and no handles. Using generalized Grunsky operators, we define a period mapping from the infinite-dimensional Teichm\\\"uller space of surfaces of this type into the unit ball in the linear space of operators on an $n$-fold direct sum of Bergman spaces of the disk. We show that this period mapping is holomorphic and injective."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.06960","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"}