{"paper":{"title":"Escaping nontangentiality: Towards a controlled tangential amortized Julia-Carath\\'eodory theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.FA","authors_text":"J. E. Pascoe, Meredith Sargent, Ryan Tully-Doyle","submitted_at":"2018-09-24T20:23:50Z","abstract_excerpt":"Let $f: D \\rightarrow \\Omega$ be a complex analytic function. The Julia quotient is given by the ratio between the distance of $f(z)$ to the boundary of $\\Omega$ and the distance of $z$ to the boundary of $D.$ A classical Julia-Carath\\'eodory type theorem states that if there is a sequence tending to $\\tau$ in the boundary of $D$ along which the Julia quotient is bounded, then the function $f$ can be extended to $\\tau$ such that $f$ is nontangentially continuous and differentiable at $\\tau$ and $f(\\tau)$ is in the boundary of $\\Omega.$ We develop an extended theory when $D$ and $\\Omega$ are ta"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.09208","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"}