Quasi-projections in Teichmüller space

Details Quasi-projections in Teichmüller space Quasi-projections in Teichmüller space

1994-09-30

arxiv.org/abs/math/9409232v1

Mathematics

Geometric Topology

Scientific paper

We consider a geometric property of the closest-points projection to a geodesic in Teichm\"uller space: the projection is called contracting if arbitrarily large balls away from the geodesic project to sets of bounded diameter. (This property always holds in 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 Teichm\"uller space, and to estimates of translation distance for pseudo-Anosov maps.

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