{"paper":{"title":"Variations of Bergman Kernels for Some Explicitly Given Families of Planar Domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Yanyan Wang","submitted_at":"2012-05-25T04:34:19Z","abstract_excerpt":"We study the parameter dependence of the Bergman kernels on some planar domains depending on complex parameter \\zeta in nontrivial \"pseudoconvex\" ways. Smoothly bounded cases are studied at first: It turns out that, in an example where the domains are annuli, the Levi form for the logarithm of the Bergman kernels with respect to \\zeta approaches to 0 as the point tends to the boundary of the domain, and in another example where the domains are discs, it approaches to 1 as the point tends to the complement of a point in the boundary. Further, in contrast to this, in the cases where the boundary"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.5610","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"}