Plurisubharmonic functions and the structure of complete Kähler manifolds with nonnegative curvature

Details Plurisubharmonic functions and the structure of complete Kähler manifolds with nonnegative curvature Plurisubharmonic functions and the structure of complete Kähler manifolds with nonnegative curvature

2003-04-07

arxiv.org/abs/math/0304096v1

Mathematics

Differential Geometry

Scientific paper

In this paper, we study global properties of continuous plurisubharmonic functions on complete noncompact K\"ahler manifolds with nonnegative bisectional curvature and their applications to the structure of such manifolds. We prove that continuous plurisubharmonic functions with reasonable growth rate on such manifolds can be approximated by smooth plurisubharmonic functions through the heat flow deformation. Optimal Liouville type theorem for the plurisubharmonic functions as well as a splitting theorem in terms of harmonic functions and holomorphic functions are established. The results are then applied to prove several structure theorems on complete noncompact K\"ahler manifolds with nonnegative bisectional or sectional curvature.

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