Teichmüller spaces are not starlike. (English) Zbl 0817.30021

Krushkal, Samuel L.

Ann. Acad. Sci. Fenn., Ser. A I, Math. 20, No. 1, 167-173 (1995).

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.

Reviewer: S.L.Krushkal (Ramat-Gan)

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)

Keywords:

starlike; de Bers embedding; Schwarzian derivative