On Bounded Positive (m, p)-Circle Domains

On Bounded Positive (m, p)-Circle Domains

Let D be a bounded positive ( m, p )-circle domain in ℂ 2 . The authors prove that if dim(Iso( D ) 0 ) = 2, then D is holomorphically equivalent to a Reinhardt domain; if dim(Iso( D ) 0 ) = 4, then D is holomorphically equivalent to the unit ball in ℂ 2 . Moreover, the authors prove the Thullen’s cl...

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Veröffentlicht in:Chinese annals of mathematics. Serie B 2018-07, Vol.39 (4), p.665-682
Hauptverfasser: Li, Hongjun, Qiu, Chunhui, Xu, Yichao
Format: Artikel
Sprache:eng
Schlagworte:
Applications of Mathematics
Domains
Equivalence
Lie groups
Mathematical analysis
Mathematics
Mathematics and Statistics
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Zusammenfassung:Let D be a bounded positive ( m, p )-circle domain in ℂ 2 . The authors prove that if dim(Iso( D ) 0 ) = 2, then D is holomorphically equivalent to a Reinhardt domain; if dim(Iso( D ) 0 ) = 4, then D is holomorphically equivalent to the unit ball in ℂ 2 . Moreover, the authors prove the Thullen’s classification on bounded Reinhardt domains in ℂ 2 by the Lie group technique.
ISSN:0252-9599
1860-6261
DOI:10.1007/s11401-018-0088-2