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Extension of CR structures on three dimensional pseudoconvex CR manifolds

Published online by Cambridge University Press:  22 January 2016

Sanghyun Cho
Sanghyun Cho*
Affiliation:
Department of Mathematics, Sogang University, C. P. O. Box 1142, Seoul 121-712, Korea, shcho@ccs.sogang.ac.kr
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Abstract.

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Let be a smoothly bounded orientable pseudoconvex CR manifold of finite type and dimℝM = 3. Then we extend the given CR structure on M to an integrable almost complex structure on which is the concave side of M and M ⊂

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 152 , December 1998, pp. 97 - 129
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1998

References

[1] Akahori, A. T., A new approach to the local embedding theorem of CR structures for n ≥ 4, Mem. Amer. Math. Soc., (1987), no. 366, Amer. Math. Soc., Providence, R. I..Google Scholar
[2] Catlin, D., A Newlander-Nirenberg theorem for manifolds with boundary, Michigan Math. J., 35 (1988).CrossRefGoogle Scholar
[3] Catlin, D., Estimates of invariant metrics on pseudoconvex domains of dimension two, Math. Z., 200 (1989).Google Scholar
[4] Catlin, D., Sufficient conditions for the extension of CR structures, J. of Geom. Anal., 4 (1994), 467–538.CrossRefGoogle Scholar
[5] Cho, S., Extension of complex structures on weakly pseudoconvex compact complex manifolds with boundary, Math. Z., 211 (1992), 105–120.CrossRefGoogle Scholar
[6] Jacobowitz, H. and Treves, F., Non-realizable CR structures, Inventiones Math, 66 (1982), 231–249.Google Scholar
[7] Kohn, J. J., Pseudo-differential operators and non-elliptic problems, C. I. M. E. (1969), 159–165.Google Scholar
[8] Kohn, J. J., Boundary behavior of on weakly pseudoconvex manifolds of dimension two, J. Differ. Geom., 6 (1972), 523–542.Google Scholar
[9] Kuranishi, M., Strongly pseudoconvex CR structures over small balls, Ann. of Math., 115 (1982), 451–500.CrossRefGoogle Scholar
[10] McNeal, J., Boundary behavior of the Bergman kernel function in ℂ2 , Duke Math. J., 58 (1989), 499–512.Google Scholar
[11] Nirenberg, L., On elliptic partial differential equations, Ann. Scuola Norm. Sup. Pisa, Ser. 3, 13 (1959).Google Scholar
[12] Raymond, X. Saint, A simple Nash-Moser implicit function theorem, L’Enseignement Mathematique, 35 (1989), 217–226.Google Scholar
[13] Webster, S., On the proof of Kuranishi’s embedding theorem, Ann. Inst. Henri Poincare, 6 (1989), 183–207.Google Scholar