Thurston's weak metric on the Teichmüller space of the torus |
| |
| Authors: | Abdelhadi Belkhirat Athanase Papadopoulos Marc Troyanov |
| |
| Affiliation: | Département de Recherche Mathématique Avancée, Université Louis Pasteur and CNRS, 7 rue René Descartes, 67084 Strasbourg Cedex, France ; Département de Recherche Mathématique Avancée, Université Louis Pasteur and CNRS, 7 rue René Descartes, 67084 Strasbourg Cedex, France ; Section de Mathématiques, École Polytechnique Féderale de Lausanne, 1015 Lausanne, Switzerland |
| |
| Abstract: | 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. |
| |
| Keywords: | Teichm" uller space, Teichm" uller metric, Thurston metric, nonsymmetric metric, weak metric, hyperbolic plane, quasi-isometry |
|
| 点击此处可从《Transactions of the American Mathematical Society》浏览原始摘要信息 |
|
点击此处可从《Transactions of the American Mathematical Society》下载全文 |
|
