On a CR family of compact strongly pseudoconvex CR manifolds
2006; Lehigh University; Volume: 72; Issue: 3 Linguagem: Inglês
10.4310/jdg/1143593744
ISSN1945-743X
AutoresJimmy Xiangji Huang, Hing-Sun Luk, Stephen S.‐T. Yau,
Tópico(s)Geometry and complex manifolds
ResumoWe 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.
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