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Teichmüller spaces are not starlike. (English) Zbl 0817.30021

We consider the problem of the starlikeness of Teichmüller spaces for finite-dimensional spaces. It is shown that in high dimensions the answer is negative.

MSC:

30F60 Teichmüller theory for Riemann surfaces
32G15 Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables)
30C55 General theory of univalent and multivalent functions of one complex variable
30C62 Quasiconformal mappings in the complex plane
30F35 Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization)
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