Sum of Lyapunov exponents of the Hodge bundle with respect to the   Teichmuller geodesic flow
  We compute the sum of the positive Lyapunov exponents of the Hodge bundle with respect to the Teichmuller geodesic flow. The computation is based on the analytic Riemann-Roch Theorem and uses a comparison of determinants of flat and hyperbolic Laplacians when the underlying Riemann surface degenerates. 
Alex Eskin, Maxim Kontsevich, Anton Zorich
math.DS math.AG math.GT