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Maximal open radius for Strebel point

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Abstract

Let \(T(S)\) be the Teichmüller space of a hyperbolic Riemann surface \(S\). As is well known, when \(T(S)\) is infinite-dimensional, the set \(\mathcal {SP}\) of Strebel points is open and dense. Given a Strebel point \([f]\) in \(T(S)\), we prove that the the maximal radius of the open ball contained in \(\mathcal {SP}\) and centered at \([f]\) is \(\frac{1}{4}\log \frac{K_0([f])}{H([f])}\). It is surprising that the boundary sphere of the maximal open ball is contained in \(\mathcal {SP}\). As a consequence, any open Strebel ball has no non-Strebel points as its boundary points. The infinitesimal version is also obtained.

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Acknowledgments

The author would like to thank the referee for his comments and suggestions which improved the exposition and clarity.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, People’s Republic of China

    Guowu Yao

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  1. Guowu Yao
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Correspondence to Guowu Yao.

Additional information

Communicated by G. Teschl.

The author was supported by the National Natural Science Foundation of China (Grant No. 11271216).

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Yao, G. Maximal open radius for Strebel point. Monatsh Math 178, 311–324 (2015). https://doi.org/10.1007/s00605-014-0707-2

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  • DOI: https://doi.org/10.1007/s00605-014-0707-2

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