On substantial boundary points

Let Δ be the unit disk and T(Δ)T(Δ) the universal Teichmüller space. In this paper, we strengthen the basic Reich construction theorem, which underlies the existence of non-Strebel points [μ][μ] in T(Δ)T(Δ) having all boundary points ζ∈∂Δζ∈∂Δ to be substantial. It is shown that the set of such points [μ][μ] contains a real infinite-dimensional sub-manifold of T(Δ)T(Δ). Some applications of this result are given.