{"paper":{"title":"Poincar\\'e inequalities and quasiconformal structure on the boundary of some hyperbolic buildings","license":"","headline":"","cross_cats":["math.MG"],"primary_cat":"math.DG","authors_text":"Herv\\'e Pajot, Marc Bourdon","submitted_at":"1997-10-20T00:00:00Z","abstract_excerpt":"In this paper we shall show that the boundary $\\partial I_{p,q}$ of the hyperbolic building $I_{p,q}$ considered in M. Bourdon, \\emph{Immeubles hyperboliques, dimension conforme et rigidit\\'e de Mostow} (Geometric And Functional Analysis, Vol 7 (1997), p 245-268) admits Poincar\\'e type inequalities. Then by using Heinonen-Koskela's work, we shall prove Loewner capacity estimates for some families of curves of $\\partial I_{p,q}$ and the fact that every quasiconformal homeomorphism $f : \\partial I_{p,q} \\longrightarrow \\partial I_{p,q}$ is quasisymetric. Therefore by these results, the answers t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9710208","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"}