Hyperbolic imbedding and spaces of continuous extensions of holomorphic maps

Joseph, James E.; Kwack, Myung H.

doi:10.1007/bf02921586

Cited by 11 publications

(9 citation statements)

References 13 publications

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“…Abate [1] showed that a complex manifold X is hyperbolic iff H(D, X) C(D, X ∞ ). The following theorem unifies these two results with a common generalization since a hyperbolic complex space is hyperbolically imbedded in itself [9].…”

Section: Definition 3 [10] Let X and Y Be Complex Spaces A Familymentioning

confidence: 73%

Unifying the little Picard, Lohwater–Pommerenke and Brody theorems

Kwack

2007

Journal of Mathematical Analysis and Applications

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Section: Definition 3 [10] Let X and Y Be Complex Spaces A Familymentioning

confidence: 73%

Unifying the little Picard, Lohwater–Pommerenke and Brody theorems

Kwack

2007

Journal of Mathematical Analysis and Applications

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“…From (4) and by the above-mentioned argument, there exists j 0 ¼ j 0 ð 1 Þ such that jc ð jÞ k ðz 0 Þj a 1 r k 1 , Ej b j 0 , Ek b 0, Ez 0 A Pð0 0 ; RÞ (11). By (10) and ( 11…”

Section: Generalization Of Alexander Theorem To Complex Spacesmentioning

confidence: 87%

“…More precisely, a ''Noguchi-type convergenceextension theorem'' means a theorem on mappings analogous to the theorem of Noguchi of extending holomorphic mappings, which would keep the local uniform convergence. Recently, several Noguchi-type convergence-extension theo-rems for analytic hypersurfaces of complex manifolds have been obtained by various authors (see [11], [12], [14]).…”

Section: Introductionmentioning

confidence: 99%

Convergence and extension theorems in geometric function theory

Thai¹,

Ngoc²

2003

Kodai Math. J.

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“…Moreover, there are local peak and antipeak plurisubharmonic functions at each boundary point of by [BF,Theorem 3.1,. We end this section with obtaining other characterizations of hyperbolic points that were introduced and investigated in [JK1] and [JK2].…”

Section: Proposition 2 Let X Be a Complex Space That Is An Increasinmentioning

confidence: 99%

Hyperbolic Imbeddedness and Extensions of Holomorphic Mappings

Thai

Duc²,

Minh³

2005

Kyushu J. Math.

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Abstract. In this article, the hyperbolic imbeddedness of (not necessary relatively compact) complex subspaces of a complex space is investigated. Using these results, two theorems on extending holomorphic mappings through hypersurfaces are given. IntroductionCharacterizing hyperbolic imbeddedness in the sense of Kobayashi is one of the most important problems of hyperbolic complex analysis. Much attention has been given to this problem, and the results on this problem can be applied to many areas of mathematics, in particular to the extensions of holomorphic mappings. For details see [La] and [Ko].Recall that a complex subspace M of a complex space X is hyperbolically imbedded in X if for distinct p, q ∈ M, the closure of M, there are open setsUnfortunately, as far as we know, almost all studies of hyperbolic imbeddedness were done under the assumption on the relative compactness of M in X. Motivated by studying geometry of unbounded domains in C n , the investigation of hyperbolic imbeddedness of (not necessary relatively compact) complex subspaces of a complex space is posed. In this paper we focus on such studies and use these results to extend holomorphic mappings through hypersurfaces, hoping that our results will be useful to people working on that subject.We now give a brief outline of the content of this article. In Section 1 we review some basic notions needed later. In Section 2 we study hyperbolic imbeddedness 2000 Mathematics Subject Classification: Primary 32H05, 32H15.

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Hyperbolic imbedding and spaces of continuous extensions of holomorphic maps

Cited by 11 publications

References 13 publications

Unifying the little Picard, Lohwater–Pommerenke and Brody theorems

Unifying the little Picard, Lohwater–Pommerenke and Brody theorems

Convergence and extension theorems in geometric function theory

Hyperbolic Imbeddedness and Extensions of Holomorphic Mappings

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