Characterization of Reinhardt domains by their automorphism groups

Alexander V. Isaev; Steven G. Krantz

Characterization of Reinhardt domains by their automorphism groups

Alexander V. Isaev^*, Steven G. Krantz

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

We survey results, obtained in the past three years, on characterizing bounded (and Kobayashi-hyperbolic) Reinhardt domains by their automorphism groups. Specifically, we consider the following two situations: (i) the group is non-compact, and (ii) the dimension of the group is sufficiently large. In addition, we prove two theorems on characterizing general hyperbolic complex manifolds by the dimensions of their automorphism groups.

Original language	English
Pages (from-to)	297-308
Number of pages	12
Journal	Journal of the Korean Mathematical Society
Volume	37
Issue number	2
Publication status	Published - 2000

Cite this

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title = "Characterization of Reinhardt domains by their automorphism groups",

abstract = "We survey results, obtained in the past three years, on characterizing bounded (and Kobayashi-hyperbolic) Reinhardt domains by their automorphism groups. Specifically, we consider the following two situations: (i) the group is non-compact, and (ii) the dimension of the group is sufficiently large. In addition, we prove two theorems on characterizing general hyperbolic complex manifolds by the dimensions of their automorphism groups.",

keywords = "Automorphism groups, Equivalence problem, Hyperbolic complex manifolds, Reinhardt domains",

author = "Isaev, \{Alexander V.\} and Krantz, \{Steven G.\}",

year = "2000",

language = "English",

volume = "37",

pages = "297--308",

journal = "Journal of the Korean Mathematical Society",

issn = "0304-9914",

publisher = "Korean Mathematical Society",

number = "2",

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TY - JOUR

T1 - Characterization of Reinhardt domains by their automorphism groups

AU - Isaev, Alexander V.

AU - Krantz, Steven G.

PY - 2000

Y1 - 2000

N2 - We survey results, obtained in the past three years, on characterizing bounded (and Kobayashi-hyperbolic) Reinhardt domains by their automorphism groups. Specifically, we consider the following two situations: (i) the group is non-compact, and (ii) the dimension of the group is sufficiently large. In addition, we prove two theorems on characterizing general hyperbolic complex manifolds by the dimensions of their automorphism groups.

AB - We survey results, obtained in the past three years, on characterizing bounded (and Kobayashi-hyperbolic) Reinhardt domains by their automorphism groups. Specifically, we consider the following two situations: (i) the group is non-compact, and (ii) the dimension of the group is sufficiently large. In addition, we prove two theorems on characterizing general hyperbolic complex manifolds by the dimensions of their automorphism groups.

KW - Automorphism groups

KW - Equivalence problem

KW - Hyperbolic complex manifolds

KW - Reinhardt domains

UR - https://www.scopus.com/pages/publications/0002068331

M3 - Article

SN - 0304-9914

VL - 37

SP - 297

EP - 308

JO - Journal of the Korean Mathematical Society

JF - Journal of the Korean Mathematical Society

IS - 2

ER -

Characterization of Reinhardt domains by their automorphism groups

Abstract

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