Domains with Non-Compact Automorphism Group: A Survey

1996/12/31 by Alexander Isaev, Isaev, A. V., Steven G. Krantz +1
Mathematics · #32 #Algebraic and Geometric Analysis #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.math/9612201

openalex publication_date 1997/12/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We survey results arising from the study of domains in Cⁿ with non-compact automorphism group. Beginning with a well-known characterization of the unit ball, we develop ideas toward a consideration of weakly pseudoconvex (and even non-pseudoconvex) domains with particular emphasis on characterizations of (i) smoothly bounded domains with non-compact automorphism group and (ii) the Levi geometry of boundary orbit accumulation points. Particular attention will be paid to results derived in the past ten years.

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