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Local rigidity of the Teichmüller space with the Thurston metric

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Abstract

We show that every ℝ-linear surjective isometry between the cotangent spaces to the Teichmüller space equipped with the Thurston norm is induced by some isometry between the underlying hyperbolic surfaces. This is an analogue of Royden’s theorem concerning the Teichmüller norm.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant No. 11901241). I am grateful to Kasra Rafi for sharing with me the question about the local rigidity of the Thurston metric. I thank Weixu Su for his comments. Finally, I thank the referees for their comments and suggestions.

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  1. School of Mathematics, South China University of Technology, Guangzhou, 510641, China

    Huiping Pan

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  1. Huiping Pan
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Pan, H. Local rigidity of the Teichmüller space with the Thurston metric. Sci. China Math. 66, 1751–1766 (2023). https://doi.org/10.1007/s11425-021-2020-0

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