{"paper":{"title":"On J. C. C. Nitsche's type inequality for hyperbolic space $\\mathbf{H}^3$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"David Kalaj","submitted_at":"2012-02-20T18:18:07Z","abstract_excerpt":"Let $\\mathbf H^3$ be the hyperbolic space identified with the unit ball $\\mathbf{B}^3 = \\{x\\in \\mathbf{R}^3: |x| < 1\\}$ with the Poincar\\'e metric $d_h$ and assume that ${\\mathcal{A}}(x_0,p,q):=\\{x: p<d_h(x,x_0)< q\\}\\subset \\mathbf H^3$ is an hyperbolic annulus with the inner and outer radii $0<p<q<\\infty$. We prove that if there exists a proper hyperbolic harmonic mapping between annuli ${\\mathcal{A}}(x_0,a,b)$ and ${\\mathcal{A}}(y_0,\\alpha,\\beta)$ in the hyperbolic space $\\mathbf H^3$, then $\\beta/\\alpha>1+\\psi(a,b)$, where $\\psi$ is a positive function."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.4410","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"}