  The purpose of this paper is to establish a Nadel vanishing theorem for big
line bundles with multiplier ideal sheaves of singular metrics admitting an
analytic Zariski decomposition (such as, metrics with minimal singularities and
Siu's metrics). For this purpose, we apply the theory of harmonic integrals and
generalize Enoki's proof of Koll'ar's injectivity theorem. Moreover we
investigate the asymptotic behavior of harmonic forms with respect to a family
of regularized metrics.

Complex Variables;Algebraic Geometry;Differential Geometry