{"paper":{"title":"The exponential Teichm\\\"uller theory: Ahlfors--Hopf differentials and diffeomorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Cong Yao, Gaven Martin","submitted_at":"2024-10-30T03:33:55Z","abstract_excerpt":"We consider minimisers of the $p$-exponential conformal energy for homeomorphisms $f:R \\to S$ of finite distortion $\\IK(z,f)$ between analytically finite Riemann surfaces in a fixed homotopy class $[f_0]$,\\[ \\mE_p(f:R,S)=\\int_R \\exp(p\\IK(z,f))\\; d\\sigma(z). \\] Homeomorphic minimisers exist should the barrier be a homeomorphism of finite energy, $\\mE_p(f_0,R,S)<\\infty$. In general this problem is not variational, however the Euler-Lagrange equations show the inverses $h=f^{-1}$ of sufficiently regular stationary solutions have an associated holomorphic quadratic differential -- the Ahlfors-Hopf"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.22667","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2410.22667/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"}