Geodesic
On~orbit connectedness, orbit convexity and envelopes of holomorphy
Izvestiya. Mathematics , Tome 44 (1995) no. 2, pp. 403-413

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We are concerned with the univalence and discription of the envelope of holomorphy $E(D)$ for a domain $D$ having a compact Lie group action. Our main result is the following: Let $X$ be a holomorphic Stein $K^C$-manifold, $D\subset X$ a $K$-invariant orbit connected domain. Then $E(D)$ is schlicht and orbit convex if and only if $E(K^C\cdot D)$ is schlicht. Moreover, in this case, $E(K^C\cdot D)=K^C\cdot e(d)$. 
@article{IM2_1995_44_2_a10,
     author = {Xiang-Yu Zhou},
     title = {On~orbit connectedness, orbit convexity and envelopes of holomorphy},
     journal = {Izvestiya. Mathematics },
     pages = {403--413},
     publisher = {mathdoc},
     volume = {44},
     number = {2},
     year = {1995},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1995_44_2_a10/}
}
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Xiang-Yu Zhou. On~orbit connectedness, orbit convexity and envelopes of holomorphy. Izvestiya. Mathematics , Tome 44 (1995) no. 2, pp. 403-413. http://geodesic.mathdoc.fr/item/IM2_1995_44_2_a10/