The failure of analyticity of Hausdorff dimensions of quasi-circles of Fuchsian groups of the second kind
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- by Shengjin Huo and Shengjian Wu PDF
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Abstract:
Let $\Gamma$ be a Fuchsian group. Any $[\mu ]$ in the Teichmüller space $T(\Gamma )$ determines a quasi-circle $f_{\mu }(\partial \mathbb {D}).$ In this paper, we prove that, for any Fuchsian group $\Gamma$ of the second kind, the Hausdorff dimension $\delta ([\mu ])=dim f_{\mu }(\partial \mathbb {D})$ is not a real analytic function in $T(\Gamma )$.References
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Additional Information
- Shengjin Huo
- Affiliation: LMAM and School of Mathematical Sciences, Peking University, Beijing, 100871, People’s Republic of China
- Address at time of publication: Department of Mathematics, Tianjin Polytechnic University, Tianjin, 300387, People’s Republic of China
- Email: sjhuo@pku.edu.cn
- Shengjian Wu
- Affiliation: LMAM and School of Mathematical Sciences, Peking University, Beijing, 100871, People’s Republic of China
- Email: wusj@math.pku.edu.cn
- Received by editor(s): April 20, 2012
- Received by editor(s) in revised form: March 11, 2013, and March 13, 2013
- Published electronically: November 4, 2014
- Additional Notes: The authors were supported by the National Natural Science Foundation of China (Grant No. 11371035 and Grant No. 11401432)
- Communicated by: Jeremy Tyson
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 143 (2015), 1101-1108
- MSC (2010): Primary 30C62, 30F35, 30F60
- DOI: https://doi.org/10.1090/S0002-9939-2014-12205-2
- MathSciNet review: 3293725