{"paper":{"title":"Absorbing angles, Steiner minimal trees, and antipodality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.MG","authors_text":"Horst Martini, Konrad J. Swanepoel, P. Oloff de Wet","submitted_at":"2011-08-25T09:26:22Z","abstract_excerpt":"We give a new proof that a star $\\{op_i:i=1,...,k\\}$ in a normed plane is a Steiner minimal tree of its vertices $\\{o,p_1,...,p_k\\}$ if and only if all angles formed by the edges at o are absorbing [Swanepoel, Networks \\textbf{36} (2000), 104--113]. The proof is more conceptual and simpler than the original one.\n  We also find a new sufficient condition for higher-dimensional normed spaces to share this characterization. In particular, a star $\\{op_i: i=1,...,k\\}$ in any CL-space is a Steiner minimal tree of its vertices $\\{o,p_1,...,p_k\\}$ if and only if all angles are absorbing, which in tur"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.5046","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"}