Local rigidity of the Teichmüller space with the Thurston metric

Local rigidity of the Teichmüller space with the Thurston metric

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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Veröffentlicht in:Science China. Mathematics 2023-08, Vol.66 (8), p.1751-1766
1. Verfasser: Pan, Huiping
Format: Artikel
Sprache:eng
Schlagworte:
Applications of Mathematics
Mathematics
Mathematics and Statistics
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Zusammenfassung: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.
ISSN:1674-7283
1869-1862
DOI:10.1007/s11425-021-2020-0