  We study the lower bound for the Bergman kernel in terms of volume of
sublevel sets of the pluricomplex Green function. We show that it implies a
bound in terms of volume of the Azukawa indicatrix which can be treated as a
multidimensional version of the Suita conjecture. We also prove that the
corresponding upper bound holds for convex domains and discuss it in bigger
detail on some convex complex ellipsoids.
