{"paper":{"title":"A note on diastatic entropy and balanced metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.DG","authors_text":"Roberto Mossa","submitted_at":"2013-03-13T17:23:19Z","abstract_excerpt":"We give un upper bound Ent(\\Omega, g)<\\lambda\\ of the diastatic entropy Ent(\\Omega, g) of a complex bounded domain (\\Omega, g) in terms of the balanced condition (in Donaldson terminology) of the Kaehler metric \\lambda g. When (\\Omega, g) is a homogeneous bounded domain we show that the converse holds true, namely if Ent(\\Omega, g)<1 then g is balanced. Moreover, we explcit compute Ent(\\Omega, g) in terms of Piatetski-Shapiro constants."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.3217","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"}