Poincar 'e inequalities and quasiconformal structure on the boundary of\n some hyperbolic buildings

1997/10/19 by Marc Bourdon, Bourdon, Marc, Hervé Pajot +1 · 1 citation
Mathematics · #Analytic and geometric function theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals #Metric Geometry (math.MG) #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.math/9710208

openalex publication_date 1997/10/19 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

In this paper we shall show that the boundary \∂ I_p,q of the\nhyperbolic building I_p,q considered in M. Bourdon, \Immeubles\nhyperboliques, dimension conforme et rigidit 'e de Mostow (Geometric And\nFunctional Analysis, Vol 7 (1997), p 245-268) admits Poincar 'e type\ninequalities. Then by using Heinonen-Koskela's work, we shall prove Loewner\ncapacity estimates for some families of curves of \∂ I_p,q and the\nfact that every quasiconformal homeomorphism f : \∂ I_p,q\n longrightarrow \∂ I_p,q is quasisymetric. Therefore by these results,\nthe answers to certain questions of Heinonen and Semmes are NO.\n

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• Poincaré inequalities on hyperbolic-type spaces

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