Examples of pleating varieties for twice punctured tori

Abstract

We give an explicit description of some pleating varieties (sets with a fixed set of bending lines in the convex hull boundary) in the quasi-Fuchsian space of the twice punctured torus. In accordance with a conjecture of the second author, we show that their closures intersect Fuchsian space in the simplices of minima introduced by Kerckhoff. All computations are done using complex Fenchel-Nielsen coordinates for quasi-Fuchsian space referred to a maximal system of curves.