12 research outputs found

    K\"{a}hler-Einstein metrics on strictly pseudoconvex domains

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    The metrics of S. Y. Cheng and S.-T. Yau are considered on a strictly pseudoconvex domains in a complex manifold. Such a manifold carries a complete K\"{a}hler-Einstein metric if and only if its canonical bundle is positive. We consider the restricted case in which the CR structure on M\partial M is normal. In this case M must be a domain in a resolution of the Sasaki cone over M\partial M. We give a condition on a normal CR manifold which it cannot satisfy if it is a CR infinity of a K\"{a}hler-Einstein manifold. We are able to mostly determine those normal CR 3-manifolds which can be CR infinities. Many examples are given of K\"{a}hler-Einstein strictly pseudoconvex manifolds on bundles and resolutions.Comment: 30 pages, 1 figure, couple corrections, improved a couple example

    Some open problems concerning q

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    Analytic cohomology groups in top degrees of Zariski open sets in ℙⁿ

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    L 2

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