  We prove a Kawamata-Viehweg vanishing theorem on a normal compact Kahler
space X: if L is a nef line bundle with numerical dimension at least equal to
2, then the q-th cohomology group of K_X+L vanishes for q at least equal to the
dimension of X minus 1. As an application, a special case of the abundance
conjecture for minimal Kahler threefolds is proven: if X is a minimal Kahler
threefold (in the usual sense that K_X is nef), then the Kodaira dimension
kappa(X) is nonnegative.
