Extremal length estimates and product regions in Teichmüller space

Details Extremal length estimates and product regions in Teichmüller space Extremal length estimates and product regions in Teichmüller space

1994-07-05

arxiv.org/abs/math/9407222v1

Mathematics

Geometric Topology

Scientific paper

We study the Teichm\"uller metric on the Teichm\"uller space of a surface of finite type, in regions where the injectivity radius of the surface is small. The main result is that in such regions the Teichm\"uller metric is approximated up to bounded additive distortion by the sup metric on a product of lower dimensional spaces. The main technical tool in the proof is the use of estimates of extremal lengths of curves in a surface based on the geometry of their hyperbolic geodesic representatives.

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