J. Heinonen et P. Koskela, FROM LOCAL TO GLOBAL IN QUASI-CONFORMAL STRUCTURES, Proceedings of the National Academy of Sciences of the United Statesof America, 93(2), 1996, pp. 554-556
We exhibit a large class of metric spaces whose infinitesimal quasicon
formal structure is strong enough to capture the global quasiconformal
structure. A sufficient condition for this to happen is described in
terms of a Poincare-type inequality.