A divergent horocycle in the horofunction compactification of the Teichmüller metric
[Un horocycle divergent dans le compactifié par horofonctions de la métrique de Teichmüller]
Annales de l'Institut Fourier, Tome 73 (2023) no. 5, pp. 1885-1902.

Nous donnons un exemple d’horocycle dand l’espace de Teichmüller de la sphère épointée cinq fois qui ne converge pas dans le compactifié de Gardiner–Masur, ou, de façon équivalente, dans le compactifié par horofonctions de la métrique de Teichmüller. Comme étape intermédiaire, nous exhibons une courbe simple fermée dont la longueur extrémale est périodique mais pas constante le long de l’horocycle. L’exemple se relève à tout espace de Teichmüller de dimension complexe supérieure à un par des constructions de revêtement.

We give an example of a horocycle in the Teichmüller space of the five-times-punctured sphere that does not converge in the Gardiner–Masur compactification, or equivalently in the horofunction compactification of the Teichmüller metric. As an intermediate step, we exhibit a simple closed curve whose extremal length is periodic but not constant along the horocycle. The example lifts to any Teichmüller space of complex dimension greater than one via covering constructions.

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DOI : 10.5802/aif.3564
Classification : 32G15, 57K20
Keywords: Horocycle, horofunction, Teichmüller space, extremal length.
Mot clés : Horocycle, horofonction, espace de Teichmüller, longueur extrémale
Fortier Bourque, Maxime 1

1 Département de mathématiques et de statistique Université de Montréal 2920, chemin de la Tour, Montréal (QC) H3T 1J4 (Canada)
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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Fortier Bourque, Maxime. A divergent horocycle in the horofunction compactification of the Teichmüller metric. Annales de l'Institut Fourier, Tome 73 (2023) no. 5, pp. 1885-1902. doi : 10.5802/aif.3564. https://aif.centre-mersenne.org/articles/10.5802/aif.3564/

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