We show that for many strata of Abelian differentials in low genus the sum of Lyapunov exponents for the Teichmüller geodesic flow is the same for all Teichmüller curves in that stratum, hence equal to the sum of Lyapunov exponents for the whole stratum. This behavior is due to the disjointness property of Teichmüller curves with various geometrically defined divisors on moduli spaces of curves.
"Nonvarying sums of Lyapunov exponents of Abelian differentials in low genus." Geom. Topol. 16 (4) 2427 - 2479, 2012. https://doi.org/10.2140/gt.2012.16.2427