{"paper":{"title":"A note on Mahler's conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Carsten Sch\\\"utt, Elisabeth M. Werner, Shlomo Reisner","submitted_at":"2010-09-18T21:09:50Z","abstract_excerpt":"Let $K$ be a convex body in $\\mathbb{R}^n$ with Santal\\'o point at 0\\. We show that if $K$ has a point on the boundary with positive generalized Gau{\\ss} curvature, then the volume product $|K| |K^\\circ|$ is not minimal. This means that a body with minimal volume product has Gau{\\ss} curvature equal to 0 almost everywhere and thus suggests strongly that a minimal body is a polytope."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.3583","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"}