On Mok's uniqueness problem of holomorphic isometries from complex unit balls of maximal dimension into classical domains

We prove that every holomorphic isometric embedding, with respect to the Bergman metrics, from a complex unit ball of maximal dimension into irreducible classical bounded symmetric domain of rank at least two that is not biholomorphic to a Type IV domain is equivalent to Mok’s embedding. This completely resolves a problem of Mok.