  Extending the Labourie-Loftin correspondence, we establish, on any punctured
oriented surface of finite type, a one-to-one correspondence between convex
projective structures with specific types of ends and punctured Riemann surface
structures endowed with meromorphic cubic differentials whose poles are at the
punctures. This generalizes previous results of Loftin, Benoist-Hulin and
Dumas-Wolf.
