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On locally quasiconformal Teichmüller spaces

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Abstract

We define a universal Teichmüller space for locally quasiconformal mappings whose dilatation grows not faster than a certain rate. We prove results of existence and uniqueness for extremal mappings in the generalized Teichmüller class. Further, we analyze the circle maps that arise.

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Acknowledgements

The second named author would like to thank Professor Chen Jixiu for his many useful suggestions and help.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Northern Illinois University, Dekalb, IL, 60115, USA

    Alastair Fletcher

  2. School of Mathematics, Renmin University of China, Beijing, 100872, People’s Republic of China

    Zemin Zhou

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  1. Alastair Fletcher
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  2. Zemin Zhou
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Correspondence to Zemin Zhou.

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AF is supported by a grant from the Simons Foundation (#352034, Alastair Fletcher). ZZ is partially supported by the National Natural Science Foundation of China (Grant 11571362).

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Fletcher, A., Zhou, Z. On locally quasiconformal Teichmüller spaces. manuscripta math. 165, 105–119 (2021). https://doi.org/10.1007/s00229-020-01201-6

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  • DOI: https://doi.org/10.1007/s00229-020-01201-6

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