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

By Lei Ni, Luen-Fai Tam. 2003

57 citations recorded by the source corpus.

In this paper, we study global properties of continuous plurisubharmonic functions on complete noncompact Kahler 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 Kahler manifolds with nonnegative bisectional or sectional curvature. 0. Introduction In this paper, we are interested in the class of complete noncompact Kahler manifolds with nonnegative holomorphic bisectional curvature. We shall first give a detailed study on the properties of heat flow with plurisubharmonic functions as initial data. Then we shall use the results to prove a Liouville theorem on plurisubharmonic functions and a splitting theorem related to harmonic and holomorphic functions. All these results will then be applied to obtain structure theorems on Kahler manifolds with nonnegative sectional or holomorphic bisectional curvature. The first author was partially supported by NSF grant DMS-0328624, USA. The second author was partially supported by Earmarked Grant of Hong Kong #CUHK4032/02P. Received 05/08/2003.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/08029a23118362fa0bba1b2e6ccaa705120e51c4

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. W. H. Meeks
2. H. Rosenberg
3. Joaquín Pérez
4. L. Hauswirth
5. A. Ros
6. Benoît Daniel
7. W. Minicozzi
8. T. Colding

In Astronomy and Astrophysics

1. H. Rosenberg
2. W. H. Meeks

In Geometry and Topology

1. W. H. Meeks
2. H. Rosenberg
3. Joaquín Pérez
4. A. Ros
5. L. Hauswirth
6. Ricardo Sa Earp
7. W. Minicozzi
8. T. Colding

Citations in the corpus

• MAXIMUM PRINCIPLES AT INFINITY (2008, background): “Some earlier fundamental works on this topic can be found in the papers of Ni and Tam [ 19 ], Omari [20], and Yau [25]”