Poincaré Inequalities and Quasiconformal Structure on the Boundary of Some Hyperbolic Buildings

@inproceedings{PAJOT1999PoincarIA,
  title={Poincar{\'e} Inequalities and Quasiconformal Structure on the Boundary of Some Hyperbolic Buildings},
  author={MARC BOURDON AND HERV{\'E} PAJOT},
  year={1999}
}
  • MARC BOURDON AND HERVÉ PAJOT
  • Published 1999
In this paper we shall show that the boundary ∂Ip,q of the hyperbolic building Ip,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 ∂Ip,q and the fact that every quasiconformal homeomorphism f : ∂Ip,q −→ ∂Ip,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… CONTINUE READING
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