{"paper":{"title":"A curvature formula associated to a family of pseudoconvex domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.CV","authors_text":"Xu Wang","submitted_at":"2015-08-02T14:14:05Z","abstract_excerpt":"We shall give a definition of the curvature operator for a family of weighted Bergman spaces $\\{\\mathcal H_t\\}$ associated to a smooth family of smoothly bounded strongly pseudoconvex domains $\\{D_t\\}$. In order to study the boundary term in the curvature operator, we shall introduce the notion of geodesic curvature for the associated family of boundaries $\\{\\partial D_t\\}$. As an application, we get a variation formula for the norms of Bergman projections of currents with compact support. A flatness criterion for $\\{\\mathcal H_t\\}$ and its applications to triviality of fibrations are also giv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.00242","kind":"arxiv","version":4},"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"}