##
Quasi-projections in Teichmuller space

### Abstract

We consider a geometric property of the closest-points projection to a
geodesic in Teichmuller space: the projection is called contracting
if arbitrarily large balls disjoint from the geodesic project to sets of
bounded diameter. (This property always holds in sufficiently negatively curved
spaces.) It is shown here to hold if and only if the geodesic is
precompact, i.e. its image in the moduli space is contained in a
compact set. Some applications are given, e.g. to stability properties
of certain quasi-geodesics in Teichmuller space, and to estimates of
translation distance for pseudo-Anosov maps.

A current draft of the paper is available as a
Postscript file,

or as a
compressed Postscript file
(with gzip).
Alternatively you can look at the
dvi file.

Let me know by
email
if you would like it in some other form.

Back to home page