Lyapunov spectrum of ball quotients with applications to commensurability questions

Abstract

We determine the Lyapunov spectrum of ball quotients arising from cyclic coverings. The computations are performed by rewriting the sum of Lyapunov exponents as ratios of intersection numbers and by the analysis of the period map near boundary divisors. As a corollary, we complete the classification of commensurability classes of all presently known non-arithmetic ball quotients.