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.
Citation
Zemin Zhou. Lixin Liu. "On triangles in the universal Teichmüller space." Kodai Math. J. 36 (3) 428 - 439, October 2013. https://doi.org/10.2996/kmj/1383660690
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