The Geometry of Complex Domains

Greene, Robert E.; Kim, Kang-Tae; Krantz, Steven G.

doi:10.1007/978-0-8176-4622-6

Cited by 80 publications

(40 citation statements)

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“…It is a basic fact that for any N > 1 the holomorphic automorphism group Aut(C N ) is very big and complicated. This is in stark contrast to the situation for bounded or, more generally, hyperbolic domains in C N which have few automorphism; see Greene et al [74] for a survey of the latter topic. Major early work on understanding the group Aut(C N ) was made by Rosay and Rudin [99].…”

Section: Automorphisms Of Euclidean Spaces and Wild Embeddingsmentioning

confidence: 82%

Holomorphic Embeddings and Immersions of Stein Manifolds: A Survey

Forstnerič

2018

Springer Proceedings in Mathematics &Amp; Statistics

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In this paper we survey results on the existence of holomorphic embeddings and immersions of Stein manifolds into complex manifolds. Most of them pertain to proper maps into Stein manifolds. We include a new result saying that every continuous map X → Y between Stein manifolds is homotopic to a proper holomorphic embedding provided that dim Y > 2 dim X and we allow a homotopic deformation of the Stein structure on X.

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Section: Automorphisms Of Euclidean Spaces and Wild Embeddingsmentioning

confidence: 82%

Holomorphic Embeddings and Immersions of Stein Manifolds: A Survey

Forstnerič

2018

Springer Proceedings in Mathematics &Amp; Statistics

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“…We also remark that a classification of Reinhardt domains with a description of their automorphism groups was obtained by Shimizu [19] and Sunada [20] (see also [10,Chapter 8]). We close this section with one more remark on condition (i).…”

Section: Example 23mentioning

confidence: 95%

A generalization of the Forelli-Rudin construction and deflation identities

Yamamori

2014

Proc. Amer. Math. Soc.

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“…Hence the sequenceρ and˜ ν converges toˆ = {z ∈ C N +1 :ρ(z) < 0} in the sense of normal setconvergence (which is, in fact, the same as the classical Carathéodory kernel convergence (cf., for example, [3,8]). Note that (ˆ ,Ĵ ) is a pseudo-Siegel domain defined by Lee.…”

Section: Definition 21mentioning

confidence: 99%

On the Differential Geometric Characterization of The Lee Models

Choi

2010

J Geom Anal

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This paper pertains to the J -Hermitian geometry of model domains introduced by Lee (Mich. We first construct a Hermitian invariant metric on the Lee model and show that the invariant metric actually coincides with the Kobayashi-Royden metric, thus demonstrating an uncommon phenomenon that the Kobayashi-Royden metric is J -Hermitian in this case. Then we follow Cartan's differential-form approach and find differential-geometric invariants, including torsion invariants, of the Lee model equipped with this J -Hermitian Kobayashi-Royden metric, and present a theorem that characterizes the Lee model by those invariants, up to J -holomorphic isometric equivalence. We also present an all dimensional analysis of the asymptotic behavior of the Kobayashi metric near the strongly pseudoconvex boundary points of domains in almost complex manifolds.

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The Geometry of Complex Domains

Cited by 80 publications

References 0 publications

Holomorphic Embeddings and Immersions of Stein Manifolds: A Survey

Holomorphic Embeddings and Immersions of Stein Manifolds: A Survey

A generalization of the Forelli-Rudin construction and deflation identities

On the Differential Geometric Characterization of The Lee Models

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