{"paper":{"title":"On a family of pseudohyperbolic disks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Raymond Mortini, Rudolf Rupp","submitted_at":"2015-11-14T16:10:22Z","abstract_excerpt":"Hyperbolic geometry plays an important role within function theory of the disk. For example, via the Schwarz-Pick Lemma, the isometries of the unit disk $\\mathbb D$ with respect to this geometry are the conformal self-maps of $\\mathbb D$. In this elementary classroom note, we are interested in the collection of the pseudohyperbolic disks $D_\\rho(x,r)$ (with fixed radius $r$ and variable hyperbolic centers $-1<x<1$) and determine explicitely with function theoretic tools the enveloppe of these disks."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.04578","kind":"arxiv","version":1},"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"}