{"paper":{"title":"A boundary Schwarz Lemma for holomorphic mappings between unit balls of different dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Yang Liu, Yifei Pan, Zhihua Chen","submitted_at":"2014-11-03T18:45:48Z","abstract_excerpt":"In this paper, we give a general boundary Schwarz lemma for holomorphic mappings between unit balls in any dimensions. It is proved that if the mapping $f\\in C^{1+\\alpha}$ at $z_0\\in \\partial \\mathbb B^n$ with $f(z_0)=w_0\\in \\partial \\mathbb B^N$ for any $n,N\\geq 1$, then the Jacobian matrix $J_f(z_0)$ maps the tangent space $T_{z_0}(\\partial \\mathbb B^n)$ to $T_{w_0}(\\partial \\mathbb B^N)$, and the holomorphic tangent space $T^{(1,0)}_{z_0}(\\partial \\mathbb B^n)$ to $T^{(1,0)}_{w_0}(\\partial \\mathbb B^N)$ as well."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.0600","kind":"arxiv","version":3},"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"}