Horospheres in Teichm\"uller space and mapping class group

Weixu Su; Dong Tan

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arXiv · 1801.01812

Horospheres in Teichm\"uller space and mapping class group

Weixu Su·Dong Tan

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Abstract

We study the geometry of horospheres in Teichm\"uller space of Riemann surfaces of genus g with n punctures, where $3g-3+n\geq 2$. We show that every $C^1$-diffeomorphism of Teichm\"uller 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 Teichm\"uller metric is the extended mapping class group.

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Weixu Su, Dong Tan. 2018-01-05. Horospheres in Teichm\"uller space and mapping class group. https://arxiv.org/abs/1801.01812

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