{"paper":{"title":"A characterization of orthogonal convergence in simply connected domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.CV","authors_text":"Filippo Bracci, Herv\\'e Gaussier, Manuel D. Contreras, Santiago D\\'iaz-Madrigal","submitted_at":"2018-06-18T10:21:44Z","abstract_excerpt":"Let $\\mathbb D$ be the unit disc in $\\mathbb C$ and let $f:\\mathbb D \\to \\mathbb C$ be a Riemann map, $\\Delta=f(\\mathbb D)$. We give a necessary and sufficient condition in terms of hyperbolic distance and horocycles which assures that a compactly divergent sequence $\\{z_n\\}\\subset \\Delta$ has the property that $\\{f^{-1}(z_n)\\}$ converges orthogonally to a point of $\\partial \\mathbb D$. We also give some applications of this to the slope problem for continuous semigroups of holomorphic self-maps of $\\mathbb D$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.06582","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"}