Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 42, 2017, 755-770

SOME METRIC PROPERTIES OF THE TEICHMÜLLER SPACE OF A CLOSED SET IN THE RIEMANN SPHERE

Nishan Chatterjee

Graduate Center of the City University of New York, Department of Mathematics
365 Fifth Avenue, New York, NY 10016, U.S.A.; nchatterjee 'at' gradcenter.cuny.edu

Abstract. Let E be an infinite closed set in the Riemann sphere, and let T(E) denote its Teichmüller space. In this paper, we study some metric properties of T(E). We prove Earle's form of Teichmüller contraction for T(E), holomorphic isometries from the open unit disk into T(E), extend Earle's form of Schwarz's lemma for classical Teichmüller spaces to T(E), and finally study complex geodesics and unique extremality for T(E).

2010 Mathematics Subject Classification: Primary 32G15, 30F60; Secondary 32H02.

Key words: Teichmüller space of a closed set, Teichmüller contraction, holomorphic isometries, Schwarz's lemma, complex geodesics.

Reference to this article: N. Chatterjee: Some metric properties of the Teichmüller space of a closed set in the Riemann sphere. Ann. Acad. Sci. Fenn. Math. 42 (2017), 755-770.

Full document as PDF file

https://doi.org/10.5186/aasfm.2017.4247