Examples of domains with non-compact automorphism groups

Siqi Fu; A. V. Isaev; S. G. Krantz

doi:10.4310/MRL.1996.v3.n5.a4

Examples of domains with non-compact automorphism groups

Siqi Fu, A. V. Isaev, S. G. Krantz

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9 Scopus citations

Abstract

We give an example of a bounded, pseudoconvex, circular domain in Cℂⁿ for any n ≥ 3 with smooth real-analytic boundary and non-compact automorphism group, which is not biholomorphically equivalent to any Reinhardt domain. We also give an analogous example in ℂ², where the domain is bounded, non-pseudoconvex and such that the boundary is smooth real-analytic at all points except one and is C^1,α-smooth at the exceptional point.

Original language	English (US)
Pages (from-to)	609-617
Number of pages	9
Journal	Mathematical Research Letters
Volume	3
Issue number	5
DOIs	https://doi.org/10.4310/MRL.1996.v3.n5.a4
State	Published - 1996
Externally published	Yes

All Science Journal Classification (ASJC) codes

Mathematics(all)

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10.4310/MRL.1996.v3.n5.a4

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abstract = "We give an example of a bounded, pseudoconvex, circular domain in Cℂn for any n ≥ 3 with smooth real-analytic boundary and non-compact automorphism group, which is not biholomorphically equivalent to any Reinhardt domain. We also give an analogous example in ℂ2, where the domain is bounded, non-pseudoconvex and such that the boundary is smooth real-analytic at all points except one and is C1,α-smooth at the exceptional point.",

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year = "1996",

doi = "10.4310/MRL.1996.v3.n5.a4",

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AU - Fu, Siqi

AU - Isaev, A. V.

AU - Krantz, S. G.

PY - 1996

Y1 - 1996

N2 - We give an example of a bounded, pseudoconvex, circular domain in Cℂn for any n ≥ 3 with smooth real-analytic boundary and non-compact automorphism group, which is not biholomorphically equivalent to any Reinhardt domain. We also give an analogous example in ℂ2, where the domain is bounded, non-pseudoconvex and such that the boundary is smooth real-analytic at all points except one and is C1,α-smooth at the exceptional point.

AB - We give an example of a bounded, pseudoconvex, circular domain in Cℂn for any n ≥ 3 with smooth real-analytic boundary and non-compact automorphism group, which is not biholomorphically equivalent to any Reinhardt domain. We also give an analogous example in ℂ2, where the domain is bounded, non-pseudoconvex and such that the boundary is smooth real-analytic at all points except one and is C1,α-smooth at the exceptional point.

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DO - 10.4310/MRL.1996.v3.n5.a4

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VL - 3

SP - 609

EP - 617

JO - Mathematical Research Letters

JF - Mathematical Research Letters

IS - 5

ER -

Examples of domains with non-compact automorphism groups

Abstract

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