{"paper":{"title":"Reciprocals and Flowers in Convexity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Emanuel Milman, Liran Rotem, Vitali Milman","submitted_at":"2018-12-20T17:21:10Z","abstract_excerpt":"We study new classes of convex bodies and star bodies with unusual properties. First we define the class of reciprocal bodies, which may be viewed as convex bodies of the form \"$1/K$\". The map $K\\mapsto K^\\prime$ sending a body to its reciprocal is a duality on the class of reciprocal bodies, and we study its properties.\n  To connect this new map with the classic polarity we use another construction, associating to each convex body $K$ a star body which we call its flower and denote by $K^\\clubsuit$. The mapping $K\\mapsto K^\\clubsuit$ is a bijection between the class $\\mathcal{K}_0^n$ of conve"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.08709","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"}