Non-Strebel points and variability sets

This paper studies the subset of the non-Strebel points in the universal Teichmüller spaceT. Let z₀ ∈ Δ be a fixed point. Then we prove that for every non-Strebel pointh, there is a holomorphic curve γ: 0, 1] →T withh as its initial point satisfying the following conditions. (1) The curve γ is on a sphere centered at the base-point ofT, i.e.d _T (id, γ(t))=d _T (id, h), (t∈0, 1]). (2) For everyt ∈ (0,1], the variability set V_γ(t)z₀] of γ(t) has non-empty interior, i.e. .