On inner radii of Teichmüller spaces

Abstract

Let r be a Fuchsian group acting on the upper half plane H. and hence also on the lower half plane 1i* in the complex plane. Let Q(r) denote the complex Banach space of bounded quadratic differentials for r defined in 'H, The Teichmiiller space T(r) of r is represented by means of the Bers embedding as a bounded region in Q(r). The inner radius i(r) of T(I) is the supremum of radii of balls in Q(r) centered at the origin which are contained in T(I'}. The most general estimate for i(r) is the following ([2], [14]):