{"paper":{"title":"Bohr radius for locally univalent harmonic mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Ilgiz R Kayumov, Nail Shakirov, Saminathan Ponnusamy","submitted_at":"2017-09-14T06:31:33Z","abstract_excerpt":"We consider the class of all sense-preserving harmonic mappings $f= h+\\overline{g}$ of the unit disk $\\ID$, where $h$ and $g$ are analytic with $g(0)=0$, and determine the Bohr radius if any one of the following conditions holds: \\bee $h$ is bounded in $\\ID$. $h$ satisfies the condition ${\\rm Re}\\, h(z)\\leq 1$ in $\\mathbb{D}$ with $h(0)>0$. both $h$ and $g$ are bounded in $\\ID$. $h$ is bounded and $g'(0)=0$. \\eee We also consider the problem of determining the Bohr radius when the supremum of the modulus of the dilatation of $f$ in $\\ID$ is strictly less than $1$. In addition, we determine the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.04629","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"}