On metrics defined by length spectra on Teichmuller spaces of surfaces with boundary

Abstract

We prove that the length spectrum metric and the arc-length spectrum metric are almost-isometric on the ${\epsilon }_0$-relative part of Teichmuller spaces of surfaces with boundary.

arXiv comment31 pages, 10 figures

References in corpus (4)

• Minimal stretch maps between hyperbolic surfaces
• On Fenchel-Nielsen coordinates on Teichmüller spaces of surfaces of infinite type
• On length spectrum metrics and weak metrics on Teichmueller spaces of surfaces with boundary
• The horofunction compactification of the arc metric on Teichmüller space