{"paper":{"title":"Holomorphic maps with large images","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Bo-Yong Chen, Xu Wang","submitted_at":"2013-03-21T12:32:53Z","abstract_excerpt":"We show that each pseudoconvex domain $\\Omega\\subset {\\mathbb C}^n$ admits a holomorphic map $F$ to ${\\mathbb C}^m$ with $|F|\\le C_1 e^{C_2 \\hat{\\delta}^{-6}}$, where $\\hat{\\delta}$ is the minimum of the boundary distance and $(1+|z|^2)^{-1/2}$, such that every boundary point is a Casorati-Weierstrass point of $F$. Based on this fact, we introduce a new anti-hyperbolic concept --- universal dominability. We also show that for each $\\alpha>6$ and each pseudoconvex domain $\\Omega\\subset {\\mathbb C}^n$, there is a holomorphic function $f$ on ${\\Omega}$ with $|f|\\le C_\\alpha e^{C_\\alpha' \\hat{\\del"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.5242","kind":"arxiv","version":5},"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"}