Abstract
We obtain a result about the relation between the Thurston boundary and the relatively hyperbolic boundary of Teichmüller space. Precisely, we prove that the identity map on Teichmüller space extends to a continuous surjective map from the subset of the Thurston boundary consisting of minimal measured foliations to the relatively hyperbolic boundary. As an application, to relate the Thurston compactification and the Teichmüller compactification of Teichmüller space, we construct a new compactification of Teichmüller space which is weaker than the Thurston compactification and the Teichmüller compactification.
Funding Statement
The work was partially supported by NSFC, No: 11771456.
Acknowledgment
The author would like to thank Professor Lixin Liu for many useful suggestions and discussions. And the author would like to thank the referee for the careful reading and many valuable suggestions.
Citation
Yaozhong Shi. "On the Thurston boundary and the relatively hyperbolic boundary of Teichmüller space." Kodai Math. J. 45 (3) 358 - 368, November 2022. https://doi.org/10.2996/kmj45303
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