{"paper":{"title":"On quasim\\\"obius maps in real Banach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.CV","authors_text":"Manzi Huang, Matti Vuorinen, Xiantao Wang, Yaxiang Li","submitted_at":"2011-05-24T06:08:37Z","abstract_excerpt":"Suppose that $E$ and $E'$ denote real Banach spaces with dimension at least 2, that $D\\varsubsetneq E$ and $D'\\varsubsetneq E'$ are domains, that $f: D\\to D'$ is an $(M,C)$-CQH homeomorphism, and that $D$ is uniform. The main aim of this paper is to prove that $D'$ is a uniform domain if and only if $f$ extends to a homeomorphism $\\bar{f}: \\bar{D}\\to \\bar{D}'$ and $\\bar{f}$ is $\\eta$-QM relative to $\\partial D$. This result shows that the answer to one of the open problems raised by V\\\"ais\\\"al\\\"a from 1991 is affirmative."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.4684","kind":"arxiv","version":3},"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"}