Remote Access Conformal Geometry and Dynamics
Green Open Access

Conformal Geometry and Dynamics

ISSN 1088-4173



On the length spectrum Teichmüller spaces of Riemann surfaces of infinite type

Author: Erina Kinjo
Journal: Conform. Geom. Dyn. 22 (2018), 1-14
MSC (2010): Primary 30F60; Secondary 32G15
Published electronically: February 26, 2018
MathSciNet review: 3768110
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information


On the Teichmüller space $T(R_0)$ of a hyperbolic Riemann surface $R_0$, we consider the length spectrum metric $d_L$, which measures the difference of hyperbolic structures of Riemann surfaces. It is known that if $R_0$ is of finite type, then $d_L$ defines the same topology as that of Teichmüller metric $d_T$ on $T(R_0)$. In 2003, H. Shiga extended the discussion to the Teichmüller spaces of Riemann surfaces of infinite type and proved that the two metrics define the same topology on $T(R_0)$ if $R_0$ satisfies some geometric condition. After that, Alessandrini-Liu-Papadopoulos-Su proved that for the Riemann surface satisfying Shiga’s condition, the identity map between the two metric spaces is locally bi-Lipschitz.

In this paper, we extend their results; that is, we show that if $R_0$ has bounded geometry, then the identity map $(T(R_0),d_L) \to (T(R_0),d_T)$ is locally bi-Lipschitz.

References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Conformal Geometry and Dynamics of the American Mathematical Society with MSC (2010): 30F60, 32G15

Retrieve articles in all journals with MSC (2010): 30F60, 32G15

Additional Information

Erina Kinjo
Affiliation: Department of Mathematics, Tokyo Institute of Technology, Oh-okayama 2-12-1, Meguro-ku, Tokyo 152-8551, Japan
MR Author ID: 942104

Keywords: Length spectrum, Teichmüller metric, Riemann surface of infinite type
Received by editor(s): September 23, 2016
Received by editor(s) in revised form: October 2, 2017
Published electronically: February 26, 2018
Article copyright: © Copyright 2018 American Mathematical Society