A Thurston boundary and visual sphere of the universal Teichmüller space

A Thurston boundary of the universal Teichmüller space T(ⅅ) is the space PMLbdd(ⅅ) of projective bounded measured laminations of ⅅ. A geodesic ray in T(ⅅ) is of generalized Teichmüller-type if it shrinks the vertical foliation of a holomorphic quadratic differential. We consider the limit points in PMLbdd(ⅅ) of certain geodesic rays induced by non-integrable holomorphic quadratic differentials. In particular, we show that there is a geodesic ray in T(ⅅ), such that the limiting projective measured lamination is supported on a geodesic lamination, whose leaves are not homotopic to leaves of either vertical or horizontal foliation of the corresponding holomorphic quadratic differential.