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On orbit connectedness, orbit convexity, and envelopes of holomorphy. (English) Zbl 0835.32006

Russ. Acad. Sci., Izv., Math. 44, No. 2, 403-413 (1995) and Izv. Ross. Akad. Nauk, Ser. Mat. 58, No. 2, 195-205 (1994).
The author studies the envelope of holomorphy \(E(D)\) for a domain \(D\) having a certain Lie group action. Thus, if \(K\) is a compact real Lie group and \(K^\mathbb{C}\) is its universal complexification, if \(X\) is a Stein \(K^\mathbb{C}\)-manifold and \(D \subset X\) is a \(K\)-invariant orbit connected domain, then \(E(D)\) is schlicht and orbit convex iff \(E (K^\mathbb{C} \cdot D)\) is schlicht, in this case \(E (K^\mathbb{C} \cdot D) = K^\mathbb{C} \cdot E(D)\).

MSC:

32D10 Envelopes of holomorphy
32A07 Special domains in \({\mathbb C}^n\) (Reinhardt, Hartogs, circular, tube) (MSC2010)
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