Extremal length
estimates and product regions in Teichmuller space
Abstract
We study the Teichmuller metric on the Teichmuller 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 Teichmuller 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.
A current draft of the paper is available as a
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