Abstract
If a bounded domain \(\Omega\) in \(\mathbb{C}{^n}\) has a noncompact automorphism group, then all the orbits of the automorphism group are noncompact (Proposition 1.3.10). Thus each orbit must “go out to the boundary” of the domain \(\Omega\), since orbits are closed in \(\Omega\) (Corollary 1.3.6).
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© 2011 Springer Science+Business Media, LLC
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Greene, R.E., Kim, KT., Krantz, S.G. (2011). The Scaling Method, I. In: The Geometry of Complex Domains. Progress in Mathematics, vol 291. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4622-6_9
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DOI: https://doi.org/10.1007/978-0-8176-4622-6_9
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