{"paper":{"title":"The visual angle metric and M\\\"obius transformations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Gendi Wang, Henri Lind\\'en, Matti Vuorinen, Riku Kl\\'en","submitted_at":"2012-08-14T14:10:45Z","abstract_excerpt":"A new similarity invariant metric $v_G$ is introduced. The visual angle metric $v_G$ is defined on a domain $G\\subsetneq\\Rn$ whose boundary is not a proper subset of a line. We find sharp bounds for $v_G$ in terms of the hyperbolic metric in the particular case when the domain is either the unit ball $\\Bn$ or the upper half space $\\Hn$. We also obtain the sharp Lipschitz constant for a M\\\"obius transformation $f: G\\rightarrow G'$ between domains $G$ and $G'$ in $\\Rn$ with respect to the metrics $v_G$ and $v_{G'}$. For instance, in the case $G=G'=\\Bn$ the result is sharp."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.2871","kind":"arxiv","version":4},"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"}