## Institute for Mathematical Sciences

## Preprint ims94-11

** Y. Minsky**
* Extremal Length Estimates and Product Regions in Teichmuller Space*

Abstract: 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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