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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"math/9710208","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"1997-10-20T00:00:00Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"efe7ec9480cbb91ab0fc83f133cfe5d376f17187a5415a5f837315fa09fa6070","abstract_canon_sha256":"6e67810d5f1a4057b1d96b66443d562ae4f3692bb296139ec158e83a8f9004a9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:34.725738Z","signature_b64":"2p+RQH6BF9+GRtXZH5+8RgWF3A8Xj3/WuYvMKpTV5D+oqc3KmKMiXJm4cDjM9yt3o0PCXGCcKfM/VE9No73pCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f1cb952c373e53fe874649025615e79b10bebf87c60576a3225e1a6f874a8d66","last_reissued_at":"2026-05-18T01:05:34.724841Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:34.724841Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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