Abstract
We determine the asymptotic behaviour of extremal length along arbitrary Teichmüller rays. This allows us to calculate the endpoint in the Gardiner–Masur compactification of any Teichmüller ray. We give a proof that this compactification is the same as the horofunction compactification. An important subset of the latter is the set of Busemann points. We show that the Busemann points are exactly the limits of the Teichmüller rays, and we give a necessary and sufficient condition for a sequence of Busemann points to converge to a Busemann point. Finally, we determine the detour metric on the boundary.
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Walsh, C. The asymptotic geometry of the Teichmüller metric. Geom Dedicata 200, 115–152 (2019). https://doi.org/10.1007/s10711-018-0364-z
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DOI: https://doi.org/10.1007/s10711-018-0364-z
Keywords
- Teichmüller space
- Teichmüller metric
- Extremal length
- Horofunction boundary
- Gardiner–Masur compactification