Open Access
July 2023 A new compactification of Teichmüller space
Lixin Liu, Yaozhong Shi
Author Affiliations +
Osaka J. Math. 60(3): 683-700 (July 2023).


We construct a new compactification of Teichmüller space. We prove that this new compactification is finer than the Gardiner-Masur compactification of Teichmüller space and the action of the mapping class group on Teichmüller space extends continuously to this new compactification. We also construct some special points in the new boundary. The construction of the new compactification is based on the Hubbard-Masur theorem, which states that there is an one-to-one corresponding between holomorphic differentials and measured foliations.

Funding Statement

The work was partially supported by NSFC, No: 11771456.


The authors would like to thank the referees for the careful reading and many valuable suggestions.


Download Citation

Lixin Liu. Yaozhong Shi. "A new compactification of Teichmüller space." Osaka J. Math. 60 (3) 683 - 700, July 2023.


Received: 30 September 2021; Revised: 25 July 2022; Published: July 2023
First available in Project Euclid: 6 July 2023

MathSciNet: MR4612511

Primary: 30F60
Secondary: 32G15

Rights: Copyright © 2023 Osaka University and Osaka Metropolitan University, Departments of Mathematics

Vol.60 • No. 3 • July 2023
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