Vol. 254, No. 1, 2011

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Extension of an analytic disc and domains in 2 with noncompact automorphism group

Minju Song

Vol. 254 (2011), No. 1, 227–238
Abstract

Let Ω be a smoothly bounded domain in 2 such that the Bergman representative map near the boundary continues to be diffeomorphic up to the boundary. If such a domain admits a holomorphic automorphism group orbit accumulating at a boundary point of finite D’Angelo type 2m, we show that the domain Ω is biholomorphic to the Thullen domain

{(z,w) ∈ ℂ2 : |z|2m + |w |2 < 1}.

This result refines the well-known theorem of E. Bedford and S. Pinchuk.

Keywords
automorphism group action, Bergman representative map
Mathematical Subject Classification 2000
Primary: 32M05
Secondary: 32D15
Milestones
Received: 10 June 2010
Revised: 24 November 2010
Accepted: 27 November 2010
Published: 7 February 2012

Proposed: Kefeng Liu
Authors
Minju Song
School of Mathematics
Korea Institute for Advanced Study (KIAS)
85 Hoegiro (Cheongnyangni-dong 207-43)
Dongdaemun-gu
Seoul, 130-722
Korea