Illinois Journal of Mathematics

Strip maps of small surfaces are convex

François Guéritaud

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The strip map is a natural map from the arc complex of a bordered hyperbolic surface $S$ to the vector space of infinitesimal deformations of $S$. We prove that the image of the strip map is a convex hypersurface when $S$ is a surface of small complexity: the punctured torus or thrice punctured sphere.

Article information

Illinois J. Math., Volume 60, Number 1 (2016), 19-37.

Received: 23 June 2015
Revised: 4 April 2016
First available in Project Euclid: 21 June 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M50: Geometric structures on low-dimensional manifolds 57M60: Group actions in low dimensions


Guéritaud, François. Strip maps of small surfaces are convex. Illinois J. Math. 60 (2016), no. 1, 19--37. doi:10.1215/ijm/1498032022.

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