Journal of Differential Geometry

On a CR family of compact strongly pseudoconvex CR manifolds

Xiaojun Huang, Hing-Sun Luk, and Stephen S.T. Yau

Abstract

We study the simultaneous filling and embedding problem for a CR family of compact strongly pseudoconvex CR manifolds of dimension at least 5. We also derive, as a consequence, the normality of the Stein fibers of the filled-in Stein space under the constant dimensionality assumption of the first Kohn-Rossi cohomology group of the fiber CR manifolds. Two main ingredients for our approach are the work of Catlin on the solution of the ∂-equation with mixed boundary conditions and the work of Siu and Ling on the study of the Grauert direct image theory for a (1,1)-convex-concave family of complex spaces.

Article information

Source
J. Differential Geom., Volume 72, Number 3 (2006), 353-379.

Dates
First available in Project Euclid: 28 March 2006

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1143593744

Digital Object Identifier
doi:10.4310/jdg/1143593744

Mathematical Reviews number (MathSciNet)
MR2219938

Zentralblatt MATH identifier
1099.32009

Citation

Huang, Xiaojun; Luk, Hing-Sun; Yau, Stephen S.T. On a CR family of compact strongly pseudoconvex CR manifolds. J. Differential Geom. 72 (2006), no. 3, 353--379. doi:10.4310/jdg/1143593744. https://projecteuclid.org/euclid.jdg/1143593744


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