Local Rigidity of Teichmüller space with Thurston metric

Abstract

We show that every $\mathbb{R}$-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, which is an analogue of Royden's theorem concerning the Teichmüller metric.

arXiv commentFinal version, minor revision according to referee's report. To appear in Science China Mathematics

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• The infinitesimal and global Thurston geometry of Teichm{ü}ller space