{"paper":{"title":"Balanced metrics on the Fock-Bargmann-Hartogs domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.CV","authors_text":"Enchao Bi, Zhenhan Tu, Zhiming Feng","submitted_at":"2015-12-31T02:44:31Z","abstract_excerpt":"The Fock-Bargmann-Hartogs domain $D_{n,m}(\\mu)$ ($\\mu>0$) in $\\mathbb{C}^{n+m}$ is defined by the inequality $\\|w\\|^2<e^{-\\mu\\|z\\|^2},$ 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 introduces a K\\\"{a}hler metric $\\alpha g(\\mu;\\nu)$ $(\\alpha>0)$ on $D_{n,m}(\\mu)$, where $g(\\mu;\\nu)$ is the K\\\"{a}hler metric associated with the K\\\"{a}hler potential $\\Phi(z,w):=\\mu\\nu{\\Vert z\\Vert}^{2}-\\ln(e^{-\\mu{\\Vert z\\Vert}^{2}}-\\Vert w\\Vert^2)$ ($\\nu>-1$) on $D_{n,m}(\\mu)$. The purpose of this paper is twofold. Firstly, we obt"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.09201","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"}