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Transactions of the American Mathematical Society

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Almost-isometry between the Teichmüller metric and the length-spectrum metric on reduced moduli space for surfaces with boundary


Authors: L. Liu, H. Shiga, W. Su and Y. Zhong
Journal: Trans. Amer. Math. Soc. 369 (2017), 6429-6464
MSC (2010): Primary 30F60; Secondary 51M10
DOI: https://doi.org/10.1090/tran/6877
Published electronically: April 7, 2017
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Abstract: We show that the Teichmüller metric and the length-spectrum metric are almost-isometric on moduli space of hyperbolic surfaces with geodesic boundaries whose lengths are bounded above.


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Additional Information

L. Liu
Affiliation: Department of Mathematics, Sun Yat-Sen University, 510275, Guangzhou, People’s Republic of China
Email: mcsllx@mail.sysu.edu.cn

H. Shiga
Affiliation: Department of Mathematics, Tokyo Institute of Technology, 2-12-1 O-okayama Meguro-ku, Tokyo 158-0001, Japan
Email: shiga@math.titech.ac.jp

W. Su
Affiliation: Department of Mathematics, Fudan University, 200433, Shanghai, People’s Republic of China – and – Shanghai Center for Mathematical Sciences (SCMS), 200433, Shanghai, People’s Republic of China
Email: suwx@fudan.edu.cn

Y. Zhong
Affiliation: Shanghai Center for Mathematical Sciences (SCMS), 200433, Shanghai, People’s Republic of China
Email: zhongyl0430@gmail.com

DOI: https://doi.org/10.1090/tran/6877
Received by editor(s): March 5, 2015
Received by editor(s) in revised form: September 28, 2015
Published electronically: April 7, 2017
Additional Notes: The first and fourth authors were partially supported by NSFC No. 11271378
The second author was partially supported by JSPS KAKENHI Grant No. 16H03933
The third author was partially supported by NSFC Nos. 11671092, 11631010.
Article copyright: © Copyright 2017 American Mathematical Society

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