{"paper":{"title":"Bohr radius for subordination and $K$-quasiconformal harmonic mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Saminathan Ponnusamy, Zhihong Liu","submitted_at":"2019-05-24T16:49:07Z","abstract_excerpt":"The present article concerns the Bohr radius for $K$-quasiconformal sense-preserving harmonic mappings $f=h+\\overline{g}$ in the unit disk $\\mathbb{D}$ for which the analytic part $h$ is subordinated to some analytic function $\\varphi$, and the purpose is to look into two cases: when $\\varphi$ is convex, or a general univalent function in $\\ID$. The results state that if $h(z) =\\sum_{n=0}^{\\infty}a_n z^n$ and $g(z)=\\sum_{n=1}^{\\infty}b_n z^n$, then $$\\sum_{n=1}^{\\infty}(|a_n|+|b_n|)r^n\\leq \\dist (\\varphi(0),\\partial\\varphi(\\ID)) ~\\mbox{ for $r\\leq r^*$} $$ and give estimates for the largest po"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.10334","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"}