  Let $M$ be a complete K\"ahler manifold with nonnegative bisectional
curvature. Suppose the universal cover does not split and $M$ admits a
nonconstant holomorphic function with polynomial growth, we prove $M$ must be
of maximal volume growth. This confirms a conjecture of Ni. There are two
essential ingredients in the proof: The Cheeger-Colding theory on
Gromov-Hausdorff convergence of manifolds; the three circle theorem for
holomorphic functions.
