{"paper":{"title":"An Upper bound on the growth of Dirichlet tilings of hyperbolic spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.GR","authors_text":"Itai Benjamini, Tsachik Gelander","submitted_at":"2015-04-22T16:42:34Z","abstract_excerpt":"It is shown that the growth rate $(\\lim_r |B(r)|^{1/r})$ of any $k$ faces Dirichlet tiling of the real hyperbolic space $\\mathbb{H}^d, d>2,$ is at most $k-1-\\epsilon$, for an $\\epsilon > 0$, depending only on $k$ and $d$. We don't know if there is a universal $\\epsilon_u > 0$, such that $k-1-\\epsilon_u$ upperbounds the growth rate for any $k$-regular tiling, when $ d > 2$?"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.05873","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":""},"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"}