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

DOI:
https://doi.org/10.1090/S0002-9947-00-02549-6

Published electronically:
August 3, 2000

MathSciNet review:
1694377

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Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9947-00-02549-6

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