Journal of Differential Geometry

Plurisubharmonic Functions and the Structure of Complete Kähler Manifolds with Nonnegative Curvature

Lei Ni and Luen-Fai Tam

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Abstract

In this paper, we study global properties of continuous plurisubharmonic functions on complete noncompact Kähler 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 Kähler manifolds with nonnegative bisectional or sectional curvature.

Article information

Source
J. Differential Geom., Volume 64, Number 3 (2003), 457-524.

Dates
First available in Project Euclid: 21 July 2004

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1090427001

Digital Object Identifier
doi:10.4310/jdg/1090427001

Mathematical Reviews number (MathSciNet)
MR2032112

Zentralblatt MATH identifier
1088.32013

Citation

Ni, Lei; Tam, Luen-Fai. Plurisubharmonic Functions and the Structure of Complete Kähler Manifolds with Nonnegative Curvature. J. Differential Geom. 64 (2003), no. 3, 457--524. doi:10.4310/jdg/1090427001. https://projecteuclid.org/euclid.jdg/1090427001


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