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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Poincaré inequalities and quasiconformal structure on the boundary of some hyperbolic buildings
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by Marc Bourdon and Hervé Pajot PDF
Proc. Amer. Math. Soc. 127 (1999), 2315-2324 Request permission


In this paper we shall show that the boundary $\partial I_{p,q}$ of the hyperbolic building $I_{p,q}$ considered by M. Bourdon admits Poincaré 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 quasisymmetric. Therefore by these results, the answer to questions 19 and 20 of Heinonen and Semmes (Thirty-three YES or NO questions about mappings, measures and metrics, Conform Geom. Dyn. 1 (1997), 1–12) is NO.
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Additional Information
  • Marc Bourdon
  • Affiliation: Institut Elie Cartan, Département de mathématiques, Université de Nancy I, BP 239, 54506 Vandoeuvre les Nancy, France
  • Email:
  • Hervé Pajot
  • Affiliation: Mathematical Science Research Institute, 1000 Centennial Drive, Berkeley, California 94720-5070
  • Address at time of publication: Département de Mathématiques, Université de Cergy-Pontoise, 2 avenue Adolphe Chauvin, BP222 Pontoise, 95302 Cergy-Pontoise Cédex, France
  • Email:
  • Received by editor(s): October 28, 1997
  • Published electronically: April 9, 1999
  • Additional Notes: Parts of this work were done during a stay of the second author at MSRI. Research at MSRI is supported in part by NSF grant DMS-9022140.
  • Communicated by: Frederick W. Gehring
  • © Copyright 1999 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 127 (1999), 2315-2324
  • MSC (1991): Primary 30C65, 51E24
  • DOI:
  • MathSciNet review: 1610912