Cubic differentials and finite volume convex projective surfaces

Benoist, Yves; Hulin, Dominique

doi:10.2140/gt.2013.17.595

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Cubic differentials and finite volume convex projective surfaces

Yves Benoist and Dominique Hulin

Geometry & Topology 17 (2013) 595–620

DOI: 10.2140/gt.2013.17.595

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

Volume 17, issue 1 (2013)