Length spectra and the Teichmueller metric for surfaces with boundary

Lixin Liu; Athanase Papadopoulos; Weixu Su; Guillaume Théret

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arXiv · 0904.2370

Length spectra and the Teichmueller metric for surfaces with boundary

Lixin Liu·Athanase Papadopoulos·Weixu Su·Guillaume Théret

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Abstract

We consider some metrics and weak metrics defined on the Teichmueller space of a surface of finite type with nonempty boundary, that are defined using the hyperbolic length spectrum of simple closed curves and of properly embedded arcs, and we compare these metrics and weak metrics with the Teichmüller metric. The comparison is on subsets of Teichmüller space which we call "$ε_0$-relative $ε$-thick parts", and whose definition depends on the choice of some positive constants $ε_0$ and $ε$. Meanwhile, we give a formula for the Teichmüller metric of a surface with boundary in terms of extremal lengths of families of arcs.

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BibTeX RIS

Lixin Liu, Athanase Papadopoulos, Weixu Su, Guillaume Théret. 2009-07-22. Length spectra and the Teichmueller metric for surfaces with boundary. https://arxiv.org/abs/0904.2370

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