Horospheres in Teichmüller space and mapping class group
Annales de l'Institut Fourier, Online first, 31 p.

We study the geometry of horospheres in Teichmüller space of Riemann surfaces of genus g with n punctures, where 3g-3+n2. We show that every C 1 -diffeomorphism of Teichmüller space to itself that preserves horospheres is an element of the extended mapping class group. Using the relation between horospheres and metric balls, we obtain a new proof of Royden’s Theorem that the isometry group of the Teichmüller metric is the extended mapping class group.

Nous étudions la géométrie des horosphéres dans l’espace de Teichmüller des surfaces de Riemann de genre g avec n perforations, oú 3g-3+n2. Nous montrons que chaque C 1 -difféomorphisme de l’espace de Teichmüller dans lui-même qui préserve les horosphéres est un élément du groupe mapping class étendu. En utilisant la relation entre les horosphéres et les boules métriques, nous obtenons une nouvelle preuve du théoréme de Royden qui affirme que le groupe d’isométrie de la métrique de Teichmüller est le groupe mapping class étendu.

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Accepted:
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DOI: 10.5802/aif.3556
Classification: 32G15,  30F30,  30F60
Keywords: Extremal length; horosphere; mapping class group; Teichmüller space.
Su, Weixu 1; Tan, Dong 2

1 School of Mathematics Sun Yat-sen University 210275, Guangzhou (P. R. China)
2 Guangxi Center for Mathematical Research Guangxi University 530000, Nanning (P. R. China)
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Su, Weixu; Tan, Dong. Horospheres in Teichmüller space and mapping class group. Annales de l'Institut Fourier, Online first, 31 p.

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