Geodesic
Domains in $\mathbf C^2$ with noncompact holomorphic automorphism groops
Sbornik. Mathematics, Tome 63 (1989) no. 1, pp. 141-151 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is shown that if a bounded domain $\Omega\subset\mathbf C^2$ with real analytic boundary has a noncompact automorphism group, then it is biholomorphically equivalent to a domain $$ E_m=\{z\in\mathbf C^2\colon|z_1|^{2m}+|z_2|^2<1\} $$ for some $m\in\mathbf N$. Bibliography: 17 titles. 
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     title = {Domains in $\mathbf C^2$ with noncompact holomorphic automorphism groops},
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È. Bedford; S. I. Pinchuk. Domains in $\mathbf C^2$ with noncompact holomorphic automorphism groops. Sbornik. Mathematics, Tome 63 (1989) no. 1, pp. 141-151. http://geodesic.mathdoc.fr/item/SM_1989_63_1_a9/

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