It is known that the optimal Noether inequality  holds for every -fold of general type with . In this talk, we give a complete classification of -folds  of general type with   satisfying the above equality by giving the explicit structure of a relative canonical model of . This model coincides with the canonical model of  when . I would also introduce the second and third optimal Noether inequalities for -folds  of general type with . This is a joint work with Tong Zhang.