{"paper":{"title":"Triangulations of uniform subquadratic growth are quasi-trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.PR"],"primary_cat":"math.MG","authors_text":"Agelos Georgakopoulos, Itai Benjamini","submitted_at":"2021-06-11T14:58:11Z","abstract_excerpt":"It is known that for every $\\alpha \\geq 1$ there is a planar triangulation in which every ball of radius $r$ has size $\\Theta(r^\\alpha)$. We prove that for $\\alpha <2$ every such triangulation is quasi-isometric to a tree. The result extends to Riemannian 2-manifolds of finite genus, and to large-scale-simply-connected graphs. We also prove that every planar triangulation of asymptotic dimension 1 is quasi-isometric to a tree."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.06443","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2106.06443/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}