{"paper":{"title":"On polyharmonic univalent mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Antti Rasila, Jiaolong Chen, Xiantao Wang","submitted_at":"2013-02-08T12:50:24Z","abstract_excerpt":"In this paper, we introduce a class of complex-valued polyharmonic mappings, denoted by $HS_{p}(\\lambda)$, and its subclass $HS_{p}^{0}(\\lambda)$, where $\\lambda\\in [0,1]$ is a constant. These classes are natural generalizations of a class of mappings studied by Goodman in 1950's. We generalize the main results of Avci and Z{\\l}otkiewicz from 1990's to the classes $HS_{p}(\\lambda)$ and $HS_{p}^{0}(\\lambda)$, showing that the mappings in $HS_{p}(\\lambda)$ are univalent and sense preserving. We also prove that the mappings in $HS_{p}^{0}(\\lambda)$ are starlike with respect to the origin, and cha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.2018","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"}