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In this paper we obtain three results concerning the geometry of complete noncompact positively curved Kähler manifolds at infinity. The first one states that the order of volume growth of a complete noncompact Kähler manifold with positive bisectional curvature is at least half of the real dimension (i.e., the complex dimension). The second one states that the curvature of a complete noncompact Kähler manifold with positive bisectional curvature decays at least linearly in the average sense.doi:10.4310/pamq.2005.v1.n1.a4 fatcat:oiei2eotlbecnohiakahjnfl5a