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Cartan-Grauert theorem for tuboids with ”curvilinear” edge. (English. Russian original) Zbl 0952.32001

Math. Notes 64, No. 6, 767-777 (1998); translation from Mat. Zametki 64, No. 6, 888-901 (1998).
The author proves an analogous of the Cartan-Grauert theorem for holomorphic convexity of domains in \(\mathbb{R}^n\subset \mathbb{C}^n\) by considering tuboids which are tube type domains with totally real edge that are asymptotically approximated near the edge points by local tubes over convex cones.

MSC:

32A07 Special domains in \({\mathbb C}^n\) (Reinhardt, Hartogs, circular, tube) (MSC2010)
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References:

[1] H. Cartan, ”Variétés analytiques réelles et variétés analytiques complexes,”Bull. Soc. Math. France,85, 77–100 (1957).
[2] H. Grauert, ”On Levi’s problem and the embedding of real analytic manifolds,”Ann. of Math. (2),68, 460–472 (1958). · Zbl 0108.07804
[3] J. Bros and D. Iagolnitzer,Tuboides et structure analytique des distributions, Vol. 16, 18, Sém. Goulaouic-Lions-Schwartz (1975). · Zbl 0333.46029
[4] J. Bros and D. Iagolnitzer, ”Tuboides dans \(\mathbb{C}\) n et généralisation d’un théoréme de Grauert,”Ann. Inst. Fourier (Grenoble),26, No. 3, 49–72 (1976). · Zbl 0336.32003
[5] L. Hörmander,An Introduction to Complex Analysis in Several Variables, van Nostrand, Princeton, N.J. (1966).
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