Asymptotics of degenerations of mixed Hodge structures
  We construct a hermitian metric on the classifying spaces of graded-polarized mixed Hodge structures and prove analogs of the strong distance estimate between an admissible period map and the approximating nilpotent orbit. We also consider the asymptotic behavior of the biextension metric, the norm estimates and the asymptotics of the reduced limit Hodge filtration. 
Tatsuki Hayama and Gregory Pearlstein
math.AG