{"paper":{"title":"The Kobayashi pseudometric for the Fock-Bargmann-Hartogs domain and its application","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.CV","authors_text":"Enchao Bi, Guicong Su, Zhenhan Tu","submitted_at":"2018-12-18T12:55:42Z","abstract_excerpt":"The Fock-Bargmann-Hartogs domain $D_{n,m}$ in $\\mathbb{C}^{n+m}$ is defined by the inequality $\\|w\\|^2<e^{-\\|z\\|^2},$ where $(z,w)\\in \\mathbb{C}^n\\times \\mathbb{C}^m$, which is an unbounded non-hyperbolic domain in $\\mathbb{C}^{n+m}$. This paper mainly consists of three parts. Firstly, we give the explicit expression of geodesics of $D_{n,1}$ in the sense of Kobayashi pseudometric; Secondly, using the formula of geodesics, we calculate explicitly the Kobayashi pseudometric on $D_{1,1}$; Lastly, we establish the Schwarz lemma at the boundary for holomorphic mappings between the nonequidimension"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.07338","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"}