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.

67 pages, 13 figures. 2nd version with some errors corrected, bibliography updated, a more detailed introduction part and an improvement on the estimates in the appendix

Cited by in corpus (4)

• Entropy degeneration of convex projective surfaces
• Convex RP^2 Structures and Cubic Differentials under Neck Separation
• Coordinates on the augmented moduli space of convex RP^2 structures
• Poles of cubic differentials and ends of convex ${\mathbb{RP}}^2$-surfaces