Minimal pseudo-Anosov translation lengths on the complex of curves

Abstract

We establish bounds on the minimal asymptotic pseudo-Anosov translation lengths on the complex of curves of orientable surfaces. In particular, for a closed surface with genus $g\ge 2$, we show that there are positive constants $a_1<a_2$ such that the minimal translation length is bounded below and above by $a_1∕g^2$ and $a_2∕g^2$.