{"paper":{"title":"On Quasi-inversions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"David Kalaj, Gendi Wang, Matti Vuorinen","submitted_at":"2012-12-04T13:58:08Z","abstract_excerpt":"Given a bounded domain $D \\subset {\\mathbb R}^n$ strictly starlike with respect to $0 \\in D\\,,$ we define a quasi-inversion w.r.t. the boundary $\\partial D \\,.$ We show that the quasi-inversion is bi-Lipschitz w.r.t. the chordal metric if and only if every \"tangent line\" of $\\partial D$ is far away from the origin. Moreover, the bi-Lipschitz constant tends to $1,$ when $\\partial D$ approaches the unit sphere in a suitable way. For the formulation of our results we use the concept of the $\\alpha$-tangent condition due to F. W. Gehring and J. V\\\"ais\\\"al\\\"a (Acta Math. 1965). This condition is sh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.0721","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"}