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

Zhou, Xiang-Yu

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 \(E (K^\mathbb{C} \cdot D) = K^\mathbb{C} \cdot E(D)\).

Reviewer: E.Pascu (Bucureşti)

MSC:

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

Keywords:

envelope of holomorphy; Lie group action