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July, 2003 Plurisubharmonic Functions and the Structure of Complete Kähler Manifolds with Nonnegative Curvature
Lei Ni, Luen-Fai Tam
J. Differential Geom. 64(3): 457-524 (July, 2003). DOI: 10.4310/jdg/1090427001

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.

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Lei Ni. Luen-Fai Tam. "Plurisubharmonic Functions and the Structure of Complete Kähler Manifolds with Nonnegative Curvature." J. Differential Geom. 64 (3) 457 - 524, July, 2003. https://doi.org/10.4310/jdg/1090427001

Information

Published: July, 2003
First available in Project Euclid: 21 July 2004

zbMATH: 1088.32013
MathSciNet: MR2032112
Digital Object Identifier: 10.4310/jdg/1090427001

Rights: Copyright © 2003 Lehigh University

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Vol.64 • No. 3 • July, 2003
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