{"paper":{"title":"Quasiconformal extension of meromorphic functions with nonzero pole","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Bappaditya Bhowmik, Goutam Satpati, Toshiyuki Sugawa","submitted_at":"2015-02-18T05:43:54Z","abstract_excerpt":"In this note, we consider meromorphic univalent functions $f(z)$ in the unit disc with a simple pole at $z=p\\in(0,1)$ which have a $k$-quasiconformal extension to the extended complex plane $\\hat{\\mathbb C},$ where $0\\leq k < 1$. We denote the class of such functions by $\\Sigma_k(p)$. We first prove an area theorem for functions in this class. Next, we derive a sufficient condition for meromorphic functions in the unit disc with a simple pole at $z=p\\in(0,1)$ to belong to the class $\\Sigma_k(p)$. Finally, we give a convolution property for functions in the class $\\Sigma_k(p)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.05125","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"}