{"paper":{"title":"Meromorphic functions with small Schwarzian derivative","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Swadesh Kumar Sahoo, Vibhuti Arora","submitted_at":"2017-09-02T03:33:53Z","abstract_excerpt":"We consider the family of all meromorphic functions $f$ of the form $$ f(z)=\\frac{1}{z}+b_0+b_1z+b_2z^2+\\cdots $$ analytic and locally univalent in the puncture disk $\\mathbb{D}_0:=\\{z\\in\\mathbb{C}:\\,0<|z|<1\\}$. Our first objective in this paper is to find a sufficient condition for $f$ to be meromorphically convex of order $\\alpha$, $0\\le \\alpha<1$, in terms of the fact that the absolute value of the well-known Schwarzian derivative $S_f (z)$ of $f$ is bounded above by a smallest positive root of a non-linear equation. Secondly, we consider a family of functions $g$ of the form $g(z)=z+a_2z^2"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.00529","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"}