Quasi-projections in Teichm\"uller space
Geometric Topology
2016-09-06 v1 Dynamical Systems
Abstract
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.
Cite
@article{arxiv.math/9409232,
title = {Quasi-projections in Teichm\"uller space},
author = {Yair Minsky},
journal= {arXiv preprint arXiv:math/9409232},
year = {2016}
}