{"paper":{"title":"Area Theorems and Quasiconformal Extensions of Harmonic Mappings with a Pole","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Limei Wang, Zhijun Chen","submitted_at":"2026-06-02T08:21:32Z","abstract_excerpt":"In this paper, we study the class \\Sigma_{H}^{k}(p) of sense-preserving univalent harmonic mappings in the unit disk \\mathbb{D} that possess a simple pole at p\\in[0,1) and admit a k-quasiconformal extension to the extended complex plane for k\\in[0,1). In 2024, Bhowmik and Satpati established an area theorem and derived a sufficient condition for the k-quasiconformal extension of harmonic mappings belonging to \\Sigma_{H}^{k}(p) without logarithmic terms. Motivated by their work, we investigate the corresponding problem when a logarithmic singularity is present. Our main contributions are two-fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.03306","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.03306/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}