{"paper":{"title":"On hyperbolicity and tautness modulo an analytic subset of Hartogs domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Do Duc Thai, Mai Anh Duc, Nguyen Van Trao, Pascal J. Thomas","submitted_at":"2011-12-18T11:32:37Z","abstract_excerpt":"Let $X$ be a complex space and $H$ a positive homogeneous plurisubharmonic function $H$ on $X\\times\\C^m$. Consider the Hartogs-type domain $\\Omega_{H}(X):=\\{(z,w)\\in X\\times \\C^m:H(z,w)<1 \\}$. Let $S$ be an analytic subset of $X$. We give necessary and sufficient conditions for hyperbolicity and tautness modulo $S\\times \\C^m$ of $\\Omega_{H}(X)$, with the obvious corollaries for the special case of Hartogs domains."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.4148","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"}