{"paper":{"title":"On J. C. C. Nitsche type inequality for annuli on Riemann surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DG","authors_text":"David Kalaj","submitted_at":"2012-04-24T16:08:53Z","abstract_excerpt":"Assume that $(\\mathcal{N},\\hbar)$ and $(\\mathcal{M},\\wp)$ are two Riemann surfaces with conformal metrics $\\hbar$ and $\\wp$. We prove that if there is a harmonic homeomorphism between an annulus $\\mathcal{A}\\subset \\mathcal{N}$ with a conformal modulus $\\mathrm{Mod}(\\mathcal{A})$ and a geodesic annulus $A_\\wp(p,\\rho_1,\\rho_2)\\subset \\mathcal{M}$, then we have ${\\rho_2}/{\\rho_1}\\ge \\Psi_\\wp\\mathrm{Mod}(\\mathcal{A})^2+1,$ where $\\Psi_\\wp$ is a certain positive constant depending on the upper bound of Gaussian curvature of the metric $\\wp$. An application for the minimal surfaces is given."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.5419","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":""},"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"}