{"paper":{"title":"An extremal eigenvalue problem in K\\\"ahler geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Dmitry Jakobson, Gerasim Kokarev, Vestislav Apostolov","submitted_at":"2014-11-28T00:26:50Z","abstract_excerpt":"We study Laplace eigenvalues $\\lambda_k$ on K\\\"ahler manifolds as functionals on the space of K\\\"ahler metrics with cohomologous K\\\"ahler forms. We introduce a natural notion of a $\\lambda_k$-extremal K\\\"ahler metric and obtain necessary and sufficient conditions for it. A particular attention is paid to the $\\lambda_1$-extremal properties of K\\\"ahler-Einstein metrics of positive scalar curvature on manifolds with non-trivial holomorphic vector fields."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.7725","kind":"arxiv","version":2},"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"}