{"paper":{"title":"Extremal Kaehler-Einstein metric for two-dimensional convex bodies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.DG","authors_text":"Alexander V. Kolesnikov, Bo'az Klartag","submitted_at":"2017-10-12T17:07:29Z","abstract_excerpt":"Given a convex body $K \\subset \\mathbb{R}^n$ with the barycenter at the origin we consider the corresponding K{\\\"a}hler-Einstein equation $e^{-\\Phi} = \\det D^2 \\Phi$. If $K$ is a simplex, then the Ricci tensor of the Hessian metric $D^2 \\Phi$ is constant and equals $\\frac{n-1}{4(n+1)}$. We conjecture that the Ricci tensor of $D^2 \\Phi$ for arbitrary $K$ is uniformly bounded by $\\frac{n-1}{4(n+1)}$ and verify this conjecture in the two-dimensional case. The general case remains open."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.04618","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"}