  We show a large class of analytic submanifolds of C^n to be strongly
extremal. This generalizes V. Sprindzhuk's solution of the complex case of
Mahler's Problem, and settles complex analogues of conjectures made in the
1970s by Baker and Sprindzhuk. The proof is based on a variation of
quantitative nondivergence estimates for quasi-polynomial flows on the space of
lattices.
