## 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)

### Keywords:

Stein neighborhoods; Cartan-Grauert theorem; tuboids
Full Text:

### 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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