{"paper":{"title":"Balanced metrics on some Hartogs type domains over bounded symmetric domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.CV","authors_text":"Zhenhan Tu, Zhiming Feng","submitted_at":"2014-11-19T14:11:14Z","abstract_excerpt":"The definition of balanced metrics was originally given by Donaldson in the case of a compact polarized K\\\"{a}hler manifold in 2001, who also established the existence of such metrics on any compact projective K\\\"{a}hler manifold with constant scalar curvature. Currently, the only noncompact manifolds on which balanced metrics are known to exist are homogeneous domains. The generalized Cartan-Hartogs domain $\\big(\\prod_{j=1}^k\\Omega_j\\big)^{{\\mathbb{B}}^{d_0}}(\\mu)$ is defined as the Hartogs type domain constructed over the product $\\prod_{j=1}^k\\Omega_j$ of irreducible bounded symmetric domai"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.5232","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"}