Abstract:
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.