Journal of Differential Geometry

Poisson Equation, Poincaré-Lelong Equation and Curvature Decay on Complete Kähler Manifolds

Lei Ni, Yuguang Shi, and Luen-Fai Tam

Abstract

In the first part of this work, the Poisson equation on complete noncompact manifolds with nonnegative Ricci curvature is studied. Sufficient and necessary conditions for the existence of solutions with certain growth rates are obtained. Sharp estimates on the solutions are also derived. In the second part, these results are applied to the study of curvature decay on complete Kähler manifolds. In particular, the Poincaré-Lelong equation on complete noncompact Kähler manifolds with nonnegative holomorphic bisectional curvature is studied. Several applications are then derived, which include the Steinness of the complete Kähler manifolds with nonnegative curvature and the flatness of a class of complete Kähler manifolds satisfying a curvature pinching condition. Liouville type results for plurisubharmonic functions are also obtained.

Article information

Source
J. Differential Geom., Volume 57, Number 2 (2001), 339-388.

Dates
First available in Project Euclid: 20 July 2004

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1090348114

Digital Object Identifier
doi:10.4310/jdg/1090348114

Mathematical Reviews number (MathSciNet)
MR1879230

Zentralblatt MATH identifier
1046.53025

Citation

Ni, Lei; Shi, Yuguang; Tam, Luen-Fai. Poisson Equation, Poincaré-Lelong Equation and Curvature Decay on Complete Kähler Manifolds. J. Differential Geom. 57 (2001), no. 2, 339--388. doi:10.4310/jdg/1090348114. https://projecteuclid.org/euclid.jdg/1090348114


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