{"paper":{"title":"On canonical metrics on Cartan-Hartogs domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.FA"],"primary_cat":"math.CV","authors_text":"Zhenhan Tu, Zhiming Feng","submitted_at":"2014-03-31T12:56:18Z","abstract_excerpt":"The Cartan-Hartogs domains are defined as a class of Hartogs type domains over irreducible bounded symmetric domains. The purpose of this paper is twofold. Firstly, for a Cartan-Hartogs domain $\\Omega^{B^{d_0}}(\\mu)$ endowed with the canonical metric $g(\\mu)$, we obtain an explicit formula for the Bergman kernel of the weighted Hilbert space $\\mathcal{H}_{\\alpha}$ of square integrable holomorphic functions on $(\\Omega^{B^{d_0}}(\\mu), g(\\mu))$ with the weight $\\exp\\{-\\alpha \\varphi\\}$ (where $\\varphi$ is a globally defined K\\\"{a}hler potential for $g(\\mu)$) for $\\alpha>0$, and, furthermore, we "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.7975","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"}