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Closed geodesics and non-differentiability of the metric in infinite-dimensional Teichmüller spaces. (English) Zbl 0842.30015
Summary: We construct a closed geodesic in any infinite-dimensional Teichmüller space. The construction also leads to a proof of non-differentiability of the metric in infinite-dimensional Teichmüller spaces, which provides a negative answer to a problem of Goldberg.

MSC:
30C62 Quasiconformal mappings in the complex plane
32G15 Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables)
14H15 Families, moduli of curves (analytic)
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