Teichmüller curves in moduli space, Eisenstein series and an application to triangular billiards (Q1122688)

This paper is concerned with some special aspects of Teichmüller theory and applications to billiards. From the summary: ``There exists a Teichmüller disc \(\Delta_ n\) containing the Riemann surface of \(y^ 2+x^ n=1,\) in the genus [(n-1)/2] Teichmüller space, such that the stabilizer of \(\Delta_ n\) in the mapping class group has a fundamental domain of finite (Poincaré) volume in \(\Delta_ n\). Application is given to an asymptotic formula for the length spectrum of the billiard in isosceles triangles with angles (\(\pi\) /n,\(\pi\) /n,((n-2)/n)\(\pi)\) and to the uniform distribution of infinite billiard trajectories in the same triangles.''