In this paper we prove a gap theorem for Kähler manifolds with nonnegative orthogonal bisectional curvature and nonnegative Ricci curvature, which generalizes an earlier result of the first author [L. Ni, An optimal gap theorem, Invent. Math. 189 2012, 3, 737–761]. We also prove a Liouville theorem for plurisubharmonic functions on such a manifold, which generalizes a previous result of L.-F. Tam and the first author [L. Ni and L.-F. Tam, Plurisubharmonic functions and the structure of complete Kähler manifolds with nonnegative curvature, J. Differential Geom. 64 2003, 3, 457–524] and complements a recent result of Liu [G. Liu, Three-circle theorem and dimension estimate for holomorphic functions on Kähler manifolds, Duke Math. J. 165 2016, 15, 2899–2919].

中文翻译：

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具有非负正交二等分曲率的Kähler流形上的间隙定理

在本文中，我们证明了具有非负正交二等分曲率和非负Ricci曲率的Kähler流形的间隙定理，它推广了第一作者的早期结果。Ni，最佳间隙定理，Invent。数学。189 2012，3，737–761]。我们还证明了流形上的次亚谐波函数的一个Liouville定理，它推广了L.-F的先前结果。谭和第一作者[L. Ni和L.F. Tam，Plurisubharmonic函数和具有非负曲率的完整Kähler流形的结构，J。微分几何。64 2003，3，457–524]，并补充了Liu的最新结果[G. Liu，Kähler流形上全纯函数的三圆定理和维数估计，Duke Math。[J. 165 2016，15，2899–2919]。