{"paper":{"title":"An upper bound for the length of a Traveling Salesman path in the Heisenberg group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Raanan Schul, Sean Li","submitted_at":"2014-03-16T19:16:50Z","abstract_excerpt":"We show that a sufficient condition for a subset $E$ in the Heisenberg group (endowed with the Carnot-Carath\\'{e}odory metric) to be contained in a rectifiable curve is that it satisfies a modified analogue of Peter Jones's geometric lemma. Our estimates improve on those of \\cite{FFP}, by replacing the power $2$ of the Jones-$\\beta$-number with any power $r<4$. This complements (in an open ended way) our work \\cite{Li-Schul-beta-leq-length}, where we showed that such an estimate was necessary, but with $r=4$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.3951","kind":"arxiv","version":3},"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"}