Cubic differentials and finite volume convex projective surfaces

Benoist, Yves¹ ; Hulin, Dominique¹

¹ Département de Mathématiques, Université Paris-Sud, Bâtiment 425, Faculté des Sciences d’Orsay, 91405 Orsay Cedex, France

Geometry & topology, Tome 17 (2013) no. 1, pp. 595-620.

Résumé

We prove that there exists a natural bijection between the set of finite volume oriented convex projective surfaces with nonabelian fundamental group and the set of finite volume hyperbolic Riemann surfaces endowed with a holomorphic cubic differential with poles of order at most 2 at the cusps.

Détail

DOI : 10.2140/gt.2013.17.595

Classification : 30F30, 35J96, 53A15, 57M50, 53C56
Keywords: affine spheres, convex projective surfaces, Teichmüller spaces, cubic differentials, Monge-Ampère equations

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