A note on the density of a subset of all integrable holomorphic quadratic differentials

Let T 0(.) be the subset of the universal Teichmüller space, which consists all of the elements with boundary dilatation 1. Let SQ(.) be the unit ball of the space Q(.) of all integrable holomorphic quadratic differentials on the unit disk . and Q 0(.) be defined as Q 0(.) = {. . SQ(.): there exists a k . (0, 1) such that [k..|.|].T0(.)}. In this paper, we show that Q 0(.) is dense in SQ(.).