## 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)

### Keywords:

envelope of holomorphy; Lie group action
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