Extension theorems, non-vanishing and the existence of good minimal models.

We prove an extension theorem for effective purely log-terminal pairs ( X, S + B) of non-negative Kodaira dimension $${\kappa (K_X+S+B)\ge 0}$$ . The main new ingredient is a refinement of the Ohsawa-Takegoshi L extension theorem involving singular Hermitian metrics. [ABSTRACT FROM AUTHOR]