{"paper":{"title":"Subdivisions of rotationally symmetric planar convex bodies minimizing the maximum relative diameter","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Antonio Ca\\~nete, Salvador Segura Gomis, Uwe Schnell","submitted_at":"2015-01-16T08:18:17Z","abstract_excerpt":"In this work we study subdivisions of $k$-rotationally symmetric planar convex bodies that minimize the maximum relative diameter functional. For some particular subdivisions called $k$-partitions, consisting of $k$ curves meeting in an interior vertex, we prove that the so-called \\emph{standard $k$-partition} (given by $k$ equiangular inradius segments) is minimizing for any $k\\in\\mathbb{N}$, $k\\geq 3$. For general subdivisions, we show that the previous result only holds for $k\\leq 6$. We also study the optimal set for this problem, obtaining that for each $k\\in\\mathbb{N}$, $k\\geq 3$, it con"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.03907","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"}