## The Bergman metric on a Stein manifold with a bounded plurisubharmonic function

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- by Bo-Yong Chen and Jin-Hao Zhang PDF
- Trans. Amer. Math. Soc.
**354**(2002), 2997-3009 Request permission

## Abstract:

In this article, we use the pluricomplex Green function to give a sufficient condition for the existence and the completeness of the Bergman metric. As a consequence, we proved that a simply connected complete Kähler manifold possesses a complete Bergman metric provided that the Riemann sectional curvature $\le -A/\rho ^2$, which implies a conjecture of Greene and Wu. Moreover, we obtain a sharp estimate for the Bergman distance on such manifolds.## References

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## Additional Information

**Bo-Yong Chen**- Affiliation: Department of Applied Mathematics, Tongji University, Shanghai 200092, China
- Email: chenboy@online.sh.cn
**Jin-Hao Zhang**- Affiliation: Department of Mathematics, Fudan University, Shanghai 200433, China
- Email: zhangjhk@online.sh.cn
- Received by editor(s): August 1, 2001
- Published electronically: March 29, 2002
- Additional Notes: The first author was supported by an NSF grant TY10126005 and a grant from Tongji Univ. No. 1390104014

The second author was supported by project G1998030600 - © Copyright 2002 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**354**(2002), 2997-3009 - MSC (2000): Primary 32H10
- DOI: https://doi.org/10.1090/S0002-9947-02-02989-6
- MathSciNet review: 1897387