## Kodai Mathematical Journal

### On triangles in the universal Teichmüller space

#### Abstract

Let $\mathcal{T}$ (Δ) be the universal Teichmüller space, viewed as the set of all Teichmüller equivalent classes [f] of quasiconformal mappings f of Δ onto itself. The notion of completing triangles was introduced by F. P. Gardiner. Three points [f], [g] and [h] are called to form a completing triangle if each pair of them has a unique geodesic segment joining them. Otherwise, they form a non-completing triangle. In this paper, we construct two Strebel points [f] and [g] such that [f], [g] and [id] form a non-completing triangle. A sufficient condition for points [f], [g] and [id] to form a completing triangle is also given.

#### Article information

Source
Kodai Math. J., Volume 36, Number 3 (2013), 428-439.

Dates
First available in Project Euclid: 5 November 2013

https://projecteuclid.org/euclid.kmj/1383660690

Digital Object Identifier
doi:10.2996/kmj/1383660690

Mathematical Reviews number (MathSciNet)
MR3161548

Zentralblatt MATH identifier
1296.30034

#### Citation

Zhou, Zemin; Liu, Lixin. On triangles in the universal Teichmüller space. Kodai Math. J. 36 (2013), no. 3, 428--439. doi:10.2996/kmj/1383660690. https://projecteuclid.org/euclid.kmj/1383660690