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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Hermitian-Einstein metrics for vector bundles on complete Kähler manifolds


Authors: Lei Ni and Huaiyu Ren
Journal: Trans. Amer. Math. Soc. 353 (2001), 441-456
MSC (2000): Primary 58G11
Published electronically: August 3, 2000
MathSciNet review: 1694377
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Abstract:

In this paper, we prove the existence of Hermitian-Einstein metrics for holomorphic vector bundles on a class of complete Kähler manifolds which include Hermitian symmetric spaces of noncompact type without Euclidean factor, strictly pseudoconvex domains with Bergman metrics and the universal cover of Gromov hyperbolic manifolds etc. We also solve the Dirichlet problem at infinity for the Hermitian-Einstein equations on holomorphic vector bundles over strictly pseudoconvex domains.


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Additional Information

Lei Ni
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
Address at time of publication: Department of Mathematics, Stanford University, Stanford, California 94305
Email: lni@math.purdue.edu

Huaiyu Ren
Affiliation: Department of Mathematics, University of California, Irvine, California 92697
Email: hren@math.uci.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-00-02549-6
PII: S 0002-9947(00)02549-6
Received by editor(s): November 5, 1998
Received by editor(s) in revised form: March 5, 1999
Published electronically: August 3, 2000
Additional Notes: Research was partially supported by an NSF grant
Article copyright: © Copyright 2000 American Mathematical Society