Convergence and extension theorems in geometric function theory

Thai, Do Duc; Ngoc, Pham

doi:10.2996/kmj/1061901061

Cited by 4 publications

(3 citation statements)

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“…In [4], the authors proved several Noguchi type extension-convergence theorems in the almost complex case. We give some other variants of such theorems for almost complex maps; this generalizes the result of [17] proved in the complex case.…”

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confidence: 63%

Some characterizations of hyperbolic almost complex manifolds

Haggui

Khalfallah

2010

Ann. Polon. Math.

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confidence: 63%

Some characterizations of hyperbolic almost complex manifolds

Haggui

Khalfallah

2010

Ann. Polon. Math.

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“…In particular, in [11], D. D. Thai and P. N. Mai have proved the above theorem in case that X is a complex subspace of a hyperbolic complex space Y such that X has ∆ * -EP for Y and A is an arbitrary analytic hypersurface of a complex manifold M .…”

Section: Introductionmentioning

confidence: 98%

“…Recently, several Noguchi-type convergence-extension theorems for analytic hypersurfaces of complex manifolds have been obtained by various authors (see [5,6,11]). In particular, in [11], D. D. Thai and P. N. Mai have proved the above theorem in case that X is a complex subspace of a hyperbolic complex space Y such that X has ∆ * -EP for Y and A is an arbitrary analytic hypersurface of a complex manifold M .…”

Section: Introductionmentioning

confidence: 99%

On Weakly Hyperbolic Spaces and a Convergence-Extension Theorem in Weakly Hyperbolic Spaces

Duc

2003

Int. J. Math.

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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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Convergence and extension theorems in geometric function theory

Abstract: In this article we show several convergence and extension theorems for analytic hypersurfaces (not necessarily with normal crossings) and for closed pluripolar sets of complex manifolds. Moreover, a generalization of theorem of Alexander to complex spaces is given.

Cited by 4 publications

References 22 publications

Some characterizations of hyperbolic almost complex manifolds

Some characterizations of hyperbolic almost complex manifolds

On Weakly Hyperbolic Spaces and a Convergence-Extension Theorem in Weakly Hyperbolic Spaces

Hyperbolic Imbeddedness and Extensions of Holomorphic Mappings

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