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

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 ... View More