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On the volume growth of K\"ahler manifolds with nonnegative bisectional curvature
Let be a complete K\"ahler manifold with nonnegative bisectional
curvature. Suppose the universal cover does not split and admits a
nonconstant holomorphic function with polynomial growth, we prove 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.Comment: 12 page
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