{"paper":{"title":"A note on uniqueness boundary of holomorphic mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Nguyen Ngoc Khanh, Ninh Van Thu","submitted_at":"2016-05-04T11:41:22Z","abstract_excerpt":"In this paper, we prove Huang et al.'s conjecture stated that if $f$ is a holomorphic function on $\\Delta^+:=\\{z\\in \\mathbb C \\colon |z|<1,~\\mathrm{Im}(z)>0\\}$ with $\\mathcal{C}^\\infty$-smooth extension up to $(-1,1)$ such that $f$ maps $(-1,1)$ into a cone $\\Gamma_C:=\\{z\\in \\mathbb C\\colon |\\mathrm{Im} (z)| \\leq C|\\mathrm{Re} (z)|\\}$, for some positive number $C$, and $f$ vanishes to infinite order at $0$, then $f$ vanishes identically. In addition, some regularity properties of the Riemann mapping functions on the boundary and an example concerning Huang et al.'s conjecture are also given."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.01232","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"}