The Bergman metric on complete Kähler manifolds
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- Chen, BY. Math. Ann. (2003) 327: 339. doi:10.1007/s00208-003-0456-3
We use the existence of a bounded uniformly Hölder continuous plurisubharmonic exhaustion function to characterize the Bergman completeness of a complete Kähler manifold. As an application, we proved that any simply-connected complete Kähler manifold with sectional curvature bounded above by a negative constant is Bergman complete.