## 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