{"paper":{"title":"On the existence of Kobayashi and Bergman metrics for Model domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Nikolay Shcherbina","submitted_at":"2019-04-29T21:25:08Z","abstract_excerpt":"We prove that for a pseudoconvex domain of the form $\\mathfrak{A} = \\{(z, w) \\in \\mathbb C^2 : v > F(z, u)\\}$, where $w = u + iv$ and F is a continuous function on ${\\mathbb C}_z \\times {\\mathbb R}_u$, the following conditions are equivalent:\n  (1) The domain $\\mathfrak{A}$ is Kobayashi hyperbolic.\n  (2) The domain $\\mathfrak{A}$ is Brody hyperbolic.\n  (3) The domain $\\mathfrak{A}$ possesses a Bergman metric.\n  (4) The domain $\\mathfrak{A}$ possesses a bounded smooth strictly plurisubharmonic function, i.e. the core $\\mathfrak{c}(\\mathfrak{A})$ of $\\mathfrak{A}$ is empty.\n  (5) The graph $\\Gam"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.12950","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"}