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Let V be a smooth projective 3-fold of general type. Denote by K 3, a rational number, the self-intersection of the canonical sheaf of any minimal model of V. One defines K 3 as the canonical volume of V. Assume p  g (V) ≥ 2. We show that $$K^3\ge \frac{1}{3}$$, which is a sharp lower bound. Then we classify those V with small volume. We also give some new examples with p  g  = 2 which have maximal canonical stability index. Finally, we give an application to 4-folds of general type.

A sharp lower bound for the canonical volume of 3-folds of general type