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ON LENGTH SPECTRUM METRICS AND WEAK METRICS ON TEICHMÜLLER SPACES OF SURFACES WITH BOUNDARY (2010)
| Venue: | ANNALES ACADEMIÆ , SCIENTIARUM FENNICÆ MATHEMATICA, VOLUMEN 35, 2010, 255–274 |
| Citations: | 8 - 8 self |
BibTeX
@MISC{Liu10onlength,
author = {Lixin Liu and Athanase Papadopoulos and Weixu Su and Guillaume Théret},
title = {ON LENGTH SPECTRUM METRICS AND WEAK METRICS ON TEICHMÜLLER SPACES OF SURFACES WITH BOUNDARY},
year = {2010}
}
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Abstract
We define and study natural metrics and weak metrics on the Teichmüller space of a surface of topologically finite type with boundary. These metrics and weak metrics are associated to the hyperbolic length spectrum of simple closed curves and of properly embedded arcs in the surface. We give a comparison between the defined metrics on regions of Teichmüller space which we call ε0-relative -thick parts, for > 0 and ε0 ≥ > 0. We compare the topologies defined by these metrics on Teichmüller space and we study divergence to infinity with respect to these various metrics.
