{"paper":{"title":"A Commentary on Teichm{\\\"u}ller's paper ``Bestimmung der extremalen quasikonformen Abbildungen bei geschlossenen orientierten Riemannschen Fl{\\\"a}chen''","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.GT","authors_text":"Annette A'Campo-Neuen, Athanase Papadopoulos (IRMA), Norbert A'Campo, Vincent Alberge (IRMA)","submitted_at":"2015-10-09T09:58:31Z","abstract_excerpt":"This is a mathematical commentary on Teichm{\\\"u}ller's paper ``Bestimmung der extremalen quasikonformen Abbildungen bei geschlossenen orientierten Riemannschen Fl{\\\"a}chen'' (Determination of extremal quasiconformal maps of closed oriented Riemann surfaces). This paper is among the last (and may be the last one) that Teichm{\\\"u}ller wrote on the theory of moduli. It contains the proof of the so-called Teichm{\\\"u}ller existence theorem for a closed surface of genus at least 2. For this proof, the author defines a mapping between a space of equivalence classes of marked Riemann surfaces (the Tei"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.02609","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"}