{"paper":{"title":"On the Suita conjecture for some convex ellipsoids in $\\mathbb C^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"W{\\l}odzimierz Zwonek, Zbigniew B{\\l}ocki","submitted_at":"2014-09-17T15:18:23Z","abstract_excerpt":"It has been recently shown that for a convex domain $\\Omega$ in $\\mathbb C^n$ and $w\\in\\Omega$ the function $F_\\Omega(w):=\\big(K_\\Omega(w)\\lambda(I_\\Omega(w))\\big)^{1/n}$, where $K_\\Omega$ is the Bergman kernel on the diagonal and $I_\\Omega(w)$ the Kobayashi indicatrix, satisfies $1\\leq F_\\Omega\\leq 4$. While the lower bound is optimal, not much more is known about the upper bound. In general it is quite difficult to compute $F_\\Omega$ even numerically and the highest value of it obtained so far is $1.010182\\dots$ In this paper we present precise, although rather complicated formulas for the e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.5023","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"}