Generalization of the big Picard theorem

Kwack, Myung H.

doi:10.2307/1970678

Cited by 53 publications

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“…The mapping (A.I.1) extends holomorphically in case M is compact and has a negatively curved ds~. This basic result is due to Mrs. Kwack [8], whose proof is a variation on a previous argument of Grauert-Recksziegel. Another proof is given in Section 6 of [5]; this argument uses the Bishop-Stoll Theorem (2.2) above.…”

Section: Appendix I Survey Of Some Removable Singularity Theoremsmentioning

confidence: 79%

Two theorems on extensions of holomorphic mappings

Griffiths

1971

Invent Math

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Section: Appendix I Survey Of Some Removable Singularity Theoremsmentioning

confidence: 79%

Two theorems on extensions of holomorphic mappings

Griffiths

1971

Invent Math

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“…If dim S ^ w -2, /is continuable to a holomorphic map of Z> into X by virtue of Theorem 2.3. In case of dim S = n -1, we can prove For the proof, we need the following result of M. H. Kwack in [9]. Remark.…”

Section: Proof the Identity Map Iά M : M-» M Has A Holomorphic Extensmentioning

confidence: 99%

On Holomorphic Maps into a Taut Complex Space

Fujimoto

1972

Nagoya Mathematical Journal

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“…Abate [1] has shown that a complex space X is hyperbolic iff H(D, X) is relatively compact in C(D, X + ). After preliminaries in §1, we offer our main results in §2, providing generalizations of Picard extension theorems from [11], [14], [15], [16], [19], of the MontelCarathéodory Theorem and of a Noguchi extension-convergence theorem (see [5, p. 300], [22, pp.…”

Section: Introductionmentioning

confidence: 99%

Extension and convergence theorems for families of normal maps in several complex variables

Joseph

Kwack

1997

Proc. Amer. Math. Soc.

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Abstract. Let H(X, Y ) ( C(X, Y ) ) represent the family of holomorphic (continuous) maps from a complex (topological) space X to a complex (topological) space Y , and let(with the compact-open topology) for each complex manifold M . We show that normal maps as defined and studied by authors in various settings are, as singleton sets, uniformly normal families, and prove extension and convergence theorems for uniformly normal families. These theorems include (1) extension theorems of big Picard type for such families -defined on complex manifolds having divisors with normal crossings -which encompass results of Järvi, Kiernan, Kobayashi, and Kwack as special cases, and (2) generalizations to such families of an extension-convergence theorem due to Noguchi.

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Generalization of the big Picard theorem

Cited by 53 publications

References 1 publication

Two theorems on extensions of holomorphic mappings

Two theorems on extensions of holomorphic mappings

On Holomorphic Maps into a Taut Complex Space

Extension and convergence theorems for families of normal maps in several complex variables

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