Jf(x) = lim sup m(f(B(x, r)))/m(B(x, r)), r->0 where B(x, r) denotes the open ^-dimensional ball of radius r about x and m denotes Lebesgue measure in R. We call Lf(x) and Jf(x\ respectively, the… Expand

In this short paper, we introduce a geometry of discrete quasiconformal groups. This subject has been studied by several mathematicians, name them few, P. Tukia, G. Martin, F. Gehring, D. Sullivan.… Expand

holds. We then estimate mod R' either by means of the space analogues of the Grötzsch and Teichmüller rings or by means of spherical annuli. The two bounds we obtain are given in Theorem 3 of §17 and… Expand