Volume 17, issue 1 (2013)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Cubic differentials and finite volume convex projective surfaces

Yves Benoist and Dominique Hulin

Geometry & Topology 17 (2013) 595–620
Abstract

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.

Keywords
affine spheres, convex projective surfaces, Teichmüller spaces, cubic differentials, Monge-Ampère equations
Mathematical Subject Classification 2010
Primary: 30F30, 35J96, 53A15, 57M50, 53C56
References
Publication
Received: 12 May 2012
Accepted: 10 November 2012
Published: 8 April 2013
Proposed: Danny Calegari
Seconded: Jean-Pierre Otal, Benson Farb
Authors
Yves Benoist
Département de Mathématiques
Université Paris-Sud
Bâtiment 425
Faculté des Sciences d’Orsay
91405 Orsay Cedex
France
http://www.math.u-psud.fr/~benoist
Dominique Hulin
Département de Mathématiques
Université Paris-Sud
Bâtiment 425
Faculté des Sciences d’Orsay
91405 Orsay Cedex
France