{"paper":{"title":"On the Third Gap for Proper Holomorphic Maps between Balls","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Shanyu Ji, Wanke Yin, Xiaojun Huang","submitted_at":"2012-01-31T04:38:02Z","abstract_excerpt":"In this paper, we study the gap rigidity phenomenon for proper holomorphic maps between balls of different dimension. We show that any $F\\in prop_3({\\mathbb{B}}^n, {\\mathbb{B}} ^N)$, with $3n<N\\leq 4n-7$ and $n\\geq 7$, is equivalent to a map of the form $(G,0)$ with $G\\in Rat ({\\mathbb{B}}^n,{\\mathbb{B}}^{3n})$. The main ingredients for the proof of our main theorem are the normal form obtained by Huang-Ji-Xu and a lemma of the first author."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.6440","kind":"arxiv","version":2},"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"}