{"paper":{"title":"Harmonic maps between annuli on Riemann surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"David Kalaj","submitted_at":"2010-03-13T22:11:52Z","abstract_excerpt":"Let $\\rho_\\Sigma=h(|z|^2)$ be a metric in a Riemann surface $\\Sigma$, where $h$ is a positive real function. Let $\\mathcal H_{r_1}=\\{w=f(z)\\}$ be the family of univalent $\\rho_\\Sigma$ harmonic mapping of the Euclidean annulus $A(r_1,1):=\\{z:r_1< |z| <1\\}$ onto a proper annulus $A_\\Sigma$ of the Riemann surface $\\Sigma$, which is subject of some geometric restrictions. It is shown that if $A_{\\Sigma}$ is fixed, then $\\sup\\{r_1: \\mathcal H_{r_1}\\neq \\emptyset \\}<1$. This generalizes the similar results from Euclidean case. The cases of Riemann and of hyperbolic harmonic mappings are treated in d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.2744","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"}