Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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



Poincaré inequalities and quasiconformal structure on the boundary of some hyperbolic buildings

Authors: Marc Bourdon and Hervé Pajot
Journal: Proc. Amer. Math. Soc. 127 (1999), 2315-2324
MSC (1991): Primary 30C65, 51E24
Published electronically: April 9, 1999
MathSciNet review: 1610912
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: 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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 30C65, 51E24

Retrieve articles in all journals with MSC (1991): 30C65, 51E24

Additional Information

Marc Bourdon
Affiliation: Institut Elie Cartan, Département de mathématiques, Université de Nancy I, BP 239, 54506 Vandoeuvre les Nancy, France

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

Keywords: Hyperbolic building, Poincar\'e inequality, quasiconformal mapping
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
Article copyright: © Copyright 1999 American Mathematical Society