Belkhirat, Abdelhadi
Papadopoulos, Athanase
Troyanov, Marc
Thurston's weak metric on the Teichmüller space of the torus
Trans. Am. Math. Soc.
Trans. Am. Math. Soc.
Trans. Am. Math. Soc.
Trans. Am. Math. Soc.
357
8
Teichmüller space
Teichmüller metric
Thurston metric
nonsymmetric metric
weak metric
hyperbolic plane
quasi-isometry
2005
2005
We define and study a natural weak metric on the Teichmüller space of the torus. A similar metric has been defined by W. Thurston on the Teichmüller space of higher genus surfaces and our definition is motivated by Thurston's definition. However, we shall see that in the case of the torus, this metric has a different behaviour than on higher genus surfaces.
Trans. Am. Math. Soc.
Journal Articles
10.1090/S0002-9947-05-03735-9