Open Access
February, 2001 Poisson Equation, Poincaré-Lelong Equation and Curvature Decay on Complete Kähler Manifolds
Lei Ni, Yuguang Shi, Luen-Fai Tam
J. Differential Geom. 57(2): 339-388 (February, 2001). DOI: 10.4310/jdg/1090348114


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.


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Lei Ni. Yuguang Shi. Luen-Fai Tam. "Poisson Equation, Poincaré-Lelong Equation and Curvature Decay on Complete Kähler Manifolds." J. Differential Geom. 57 (2) 339 - 388, February, 2001.


Published: February, 2001
First available in Project Euclid: 20 July 2004

zbMATH: 1046.53025
MathSciNet: MR1879230
Digital Object Identifier: 10.4310/jdg/1090348114

Rights: Copyright © 2001 Lehigh University

Vol.57 • No. 2 • February, 2001
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