Asymptotic Behavior of Normal Mappings of Several Complex Variables
Let M and N be connected Hermitian manifolds of dimensions m and n with Hermitian metrics hM and hN, respectively. Then the space ℓ(M, N) of continuous mappings between M and N endowed with the compact-open topology is second countable so that a metric can be furnished in ℓ(M, N) which induces the c...
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| Veröffentlicht in: | Canadian journal of mathematics Jg. 36; H. 4; S. 718 - 746 |
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| 1. Verfasser: | |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge, UK
Cambridge University Press
01.08.1984
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| ISSN: | 0008-414X, 1496-4279 |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | Let M and N be connected Hermitian manifolds of dimensions m and n with Hermitian metrics hM
and hN, respectively. Then the space ℓ(M, N) of continuous mappings between M and N endowed with the compact-open topology is second countable so that a metric can be furnished in ℓ(M, N) which induces the compact-open topology. A sequence {fn} in ℓ(M, N) converges to a n f in ℓ(M, N) in this topology if and only if fn
converges to f uniformly on compact subsets of M. It is then an easy consequence of the Cauchy integral formula to show that the space ℋ(M, N) of holomorphic mappings f:M → N is a closed subspace of ℓ(M, N). In this paper, generalizing the classical notions of normal functions, Bloch functions, regular sequences and P-point sequences of one complex variable to the mappings in ℋ(M, N), see also [25], we obtain various relations which exist between these notions. |
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| ISSN: | 0008-414X 1496-4279 |
| DOI: | 10.4153/CJM-1984-041-9 |