## Illinois Journal of Mathematics

### Strip maps of small surfaces are convex

François Guéritaud

#### Abstract

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

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

Dates
Revised: 4 April 2016
First available in Project Euclid: 21 June 2017

https://projecteuclid.org/euclid.ijm/1498032022

Digital Object Identifier
doi:10.1215/ijm/1498032022

Mathematical Reviews number (MathSciNet)
MR3665170

Zentralblatt MATH identifier
1372.57034

#### Citation

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