Slowly divergent geodesics in moduli space
Abstract
Description
Slowly divergent geodesics in the moduli space of Riemann surfaces of genus at least 2 are constructed via cyclic branched covers of the torus. Nonergodic examples (i.e. geodesics whose defining quadratic differential has nonergodic vertical foliation) diverging to infinity at sublinear rates are constructed using a Diophantine condition. Examples with an arbitrarily slow prescribed growth rate are also exhibited.
26 pages, no figures
26 pages, no figures