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.

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

References in corpus (5)

• Convexity of length functions and Thurston's shear coordinates
• Generalized stretch lines for surfaces with boundary
• Optimal Lipschitz Maps on One-holed Tori and the Thurston Metric Theory of Teichmueller Space
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Cited by in corpus (1)

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