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


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


Zbl 0362.53049
Full Text: DOI


[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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