{"paper":{"title":"$L^p$-Extremal Teichm\\\"uller mappings between Riemann surfaces are diffeomorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CV","authors_text":"Cong Yao, Gaven Martin","submitted_at":"2026-07-04T23:01:39Z","abstract_excerpt":"We consider minimisers in the homotopy class of a homeomorphism $f_0:R\\to S$ between analytically finite Riemann surfaces with minimal $L^p$- conformal energy \\[ \\mathsf{E}_p(f:R,S)=\\int_R \\IK^p(z,f)\\; d\\sigma_R(z). \\] The problem was first raised by Ahlfors in his celebrated proof of Teichm\\\"uller's theorem-the case $p=\\infty$, but the existence, topological regularity and analytic regularity of these $L^p$ minimisers remained unknown for all $1<p<\\infty$. Ahlfors established weak existence for $p\\geq 2$. Here we prove that for all p, $1\\leq p<\\infty$, such minimisers exist, are unique and ar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.04051","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.04051/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}