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

Proceedings of the American Mathematical Society

Volumn 127, Issue 8, 1999, Pages 2315-2324

  Bourdon, Marc ^a,c   Pajot, Hervé ^a,b  

^a UNIVERSITÉ HENRI POINCARÉ NANCY 1   (France)

^b MATHEMATICAL SCIENCES RESEARCH INSTITUTE   (United States)

^c UNIVERSITÉ DE CERGY PONTOISE   (France)

Author keywords

Hyperbolic building; Poincar inequality; Quasiconformal mapping

Indexed keywords

EID: 22644452019     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9939-99-04901-1     Document Type: Article

References (15)

1. M. Bourdon, Immeubles hyperboliques, dimension conforme et rigidité de Mostow, Geometric And Functional Analysis, Vol. 7 (1997), 245-268. MR 98c:20056
2. K. S. Brown, Buildings, Springer-Verlag (1989). MR 90e:20001
3. M. Coornaert, T. Delzant, A. Papadopoulos, Géométrie et théorie des groupes, les groupes hyperboliques de M. Gromov, Lecture Notes in Mathematics 1441, Springer-Verlag (1991). MR 92f:57003
4. F. W. Gehring, The definitions and exceptional sets for quasiconformal mappings, Annales Academiae Scientiarum Fennicae Ser. A1 281 (1960), 1-28. MR 23:A1800
5. D. Gilbarg, N. S. Trudinger, Elliptic partial differential equations of second order, Springer-Verlag (1983). MR 86c:35035
6. P. Hajlasz, P. Koskela, Sobolev meets Poincaré, Compte Rendus de l'Académie des Sciences de Paris 320 (1995), 1211-1215. MR 96f:46062
7. J. Heinonen, P. Koskela, Definitions of quasiconformality, Inventiones Mathematicae 120 (1995), 61-79. MR 96e:30051
8. _, Quasiconformal maps in metric spaces with controlled geometry, Acta Mathematica, to appear.
9. J. Heinonen, S. Sommes, Thirty-three YES or NO questions about mappings, measures and metrics, Conformal geometry and dynamics (electronic journal of the American Mathematical Society), Vol. 1 (1997), 1-12. CMP 97:13
10. P. Mattila, Geometry of sets and measures in Euclidean spaces, Cambridge Studies in Advanced Mathematics, vol. 44, Cambridge University Press (1995) MR 96h:28006
11. F. Paulin, Un groupe hyperbolique est déterminé par son bord, Journal of the London Mathematical Society, vol. 54 (1996), 50-74. MR 97d:20042
12. M. Ronan, Lectures on buildings, Academic Press (1988). MR 90j:20001
13. S. Semmes, Finding curves on general metric spaces through quantitative topology, with applications for Sobolev and Poincaré inequalities, Selecta Mathematica, vol. 2, (1996), 155-295. MR 97j:46033
14. J. Väisälä, Lectures on n-dimensional quasiconformal mappings, Lecture Notes in Mathematics 229, Springer-Verlag (1971). MR 56:12260
15. _, Quasimöbius maps, Journal d'Analyse Mathématique, Vol. 44 (1984/1985), 218-234. MR 87f:30059