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On the existence of a complete Kähler metric on non-compact complex manifolds and the regularity of Fefferman’s equation. (English) Zbl 0506.53031


MSC:

53C55 Global differential geometry of Hermitian and Kählerian manifolds
32T99 Pseudoconvex domains
32Q99 Complex manifolds
58D17 Manifolds of metrics (especially Riemannian)

Citations:

Zbl 0362.53049
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References:

[1] and , The Dirichlet problem for an equation of complex Monge Ampère type, in Proceedings of the Park City Conference on Geometry and P.D.E., to appear.
[2] Cheng, Comm. Pure Appl. Math. 28 pp 333– (1975)
[3] Fefferman, Ann. of Math. 103 pp 395– (1976)
[4] Kähler metrics of negative curvature, the Bergman metric near the boundary, and the Kobayashi metric on smooth bounded strictly pseudoconvex sets, preprint. · Zbl 0422.53032
[5] Koeber, Proc. Amer. Math. Soc. 9 pp 452– (1958)
[6] Multiple Integrals in the Calculus of Variations, Springer-Verlag, New York, 1966. · Zbl 0142.38701
[7] Yau, Comm. Pure Appl. Math. 28 pp 201– (1975)
[8] Yau, Amer. J. Math. 100 pp 197– (1978)
[9] Yau, Comm. Pure Appl. Math. 31 pp 339– (1978)
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