{"paper":{"title":"Rawnsley's $\\varepsilon$-function on some Hartogs type domains over bounded symmetric domains and its applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Enchao Bi, Guicong Su, Zhenhan Tu, Zhiming Feng","submitted_at":"2018-11-12T13:04:45Z","abstract_excerpt":"The purpose of this paper is twofold. Firstly, we will compute the explicit expression of the Rawnsley's $\\varepsilon$-function $\\varepsilon_{(\\alpha,g(\\mu;\\nu))}$ of $\\big(\\big(\\prod_{j=1}^k\\Omega_j\\big)^{{\\mathbb{B}}^{d_0}}(\\mu),g(\\mu;\\nu)\\big)$, where $g(\\mu;\\nu)$ is a K\\\"ahler metric associated with the K\\\"ahler potential $-\\sum_{j=1}^k\\nu_j\\ln N_{\\Omega_j}(z_j,\\overline{z_j})^{\\mu_j}-\\ln(\\prod_{j=1}^kN_{\\Omega_j}(z_j,\\overline{z_j})^{\\mu_j}-\\|w\\|^2)$ on the generalized Cartan-Hartogs domain $\\big(\\prod_{j=1}^k\\Omega_j\\big)^{{\\mathbb{B}}^{d_0}}(\\mu)$ and obtain necessary and sufficient con"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.04703","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"}