{"paper":{"title":"Local properties of quasihyperbolic and freely quasiconformal mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Matti Vuorinen, Xiantao Wang, Yaxiang Li","submitted_at":"2011-10-28T07:29:16Z","abstract_excerpt":"Suppose that $E$ and $E'$ denote real Banach spaces with dimension at least 2, that $D\\subset E$ and $D'\\subset E'$ are domains, and that $f: D\\to D'$ is a homeomorphism. In this paper, we prove that if there exists some constant $M>1$ (resp. some homeomorphism $\\phi$) such that for all $x\\in D$, $f: B(x,d_D(x))\\to f(B(x,d_D(x)))$ is $M$-QH (resp. $\\phi$-FQC), then $f$ is $M_1$-QH with $M_1=M_1(M)$ (resp. $\\phi_1$-FQC with $\\phi_1=\\phi_1(\\phi)$). We apply our results to establish, in terms of the $j_D$ metric, a sufficient condition for a homeomorphism to be FQC."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.6269","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"}