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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Completion of Akahori's construction of the versal family of strongly pseudoconvex CR structures


Author: Kimio Miyajima
Journal: Trans. Amer. Math. Soc. 277 (1983), 163-172
MSC: Primary 32G07
DOI: https://doi.org/10.1090/S0002-9947-1983-0690046-5
MathSciNet review: 690046
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Abstract: Let $ M$ be a compact smooth boundary of a strongly pseudo-convex domain of a complex manifold $ N$ with dim $ N \geqslant 4$. We established a sharp a priori estimate for the Laplacian operator associated with Akahori's subcomplex of the $ T'{N_{\vert M}}$-valued $ {\bar \partial _b}$-complex to construct the complex analytic versal family (in the sense of Kuranishi) of $ CR$ structures of class $ {C^\infty }$ on $ M$.


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DOI: https://doi.org/10.1090/S0002-9947-1983-0690046-5
Keywords: $ CR$ structure, deformation, strongly pseudo-convex boundary, versal family
Article copyright: © Copyright 1983 American Mathematical Society