Meromorphic cubic differentials and convex projective structures

Abstract

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.