Geometry & Topology

Cubic differentials and finite volume convex projective surfaces

Yves Benoist and Dominique Hulin

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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.

Article information

Geom. Topol., Volume 17, Number 1 (2013), 595-620.

Received: 12 May 2012
Accepted: 10 November 2012
First available in Project Euclid: 20 December 2017

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Zentralblatt MATH identifier

Primary: 30F30: Differentials on Riemann surfaces 35J96: Elliptic Monge-Ampère equations 53A15: Affine differential geometry 57M50: Geometric structures on low-dimensional manifolds 53C56: Other complex differential geometry [See also 32Cxx]

affine spheres convex projective surfaces Teichmüller spaces cubic differentials Monge-Ampère equations


Benoist, Yves; Hulin, Dominique. Cubic differentials and finite volume convex projective surfaces. Geom. Topol. 17 (2013), no. 1, 595--620. doi:10.2140/gt.2013.17.595.

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