On length spectrum metrics and weak metrics on Teichmueller spaces of surfaces with boundary

Lixin Liu; Athanase Papadopoulos; Weixu Su; Guillaume Théret

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arXiv · 0903.0744

On length spectrum metrics and weak metrics on Teichmueller spaces of surfaces with boundary

Lixin Liu·Athanase Papadopoulos·Weixu Su·Guillaume Théret

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Abstract

We define and study metrics and weak metrics on the Teichmueller 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 Teichmueller space which we call $\varepsilon_0$-relative $ε$-thick parts} for $ε>0$ and $\varepsilon_0\geq ε>0$.

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Lixin Liu, Athanase Papadopoulos, Weixu Su, Guillaume Théret. 2009-03-04. On length spectrum metrics and weak metrics on Teichmueller spaces of surfaces with boundary. https://arxiv.org/abs/0903.0744

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