A note on holomorphic quadratic differentials on the unit disk

Abstract

Let Q(Δ) be the set of all integrable holomorphic quadratic differentials on the unit disk Δ. The subset Q₀(Δ) of Q(Δ) is the set associated with T₀ classes in the universal Teichmüller space T(Δ). In this paper, it is shown that Q₀(Δ) is dense in Q(Δ). The infinitesimal version is also obtained.