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- Title
APPROXIMATION OF HOLOMORPHIC MAPPINGS ON 1-CONVEX DOMAINS.
- Authors
STOPAR, KRIS
- Abstract
Let π : Z → X be a holomorphic submersion of a complex manifold Z onto a complex manifold X and D ⋐ X a 1-convex domain with strongly pseudoconvex boundary. We prove that under certain conditions there always exists a spray of π-sections over which has prescribed core, it fixes the exceptional set E of D, and is dominating on . Each section in this spray is of class and holomorphic on D. As a consequence we obtain several approximation results for π-sections. In particular, we prove that π-sections which are of class and holomorphic on D can be approximated in the topology by π-sections that are holomorphic in open neighborhoods of . Under additional assumptions on the submersion we also get approximation by global holomorphic π-sections and the Oka principle over 1-convex manifolds. We include an application to the construction of proper holomorphic maps of 1-convex domains into q-convex manifolds.
- Subjects
HOLOMORPHIC functions; APPROXIMATION theory; CONVEX domains; SUBMERSIONS (Mathematics); COMPLEX manifolds; SET theory; PROOF theory
- Publication
International Journal of Mathematics, 2013, Vol 24, Issue 14, p-1
- ISSN
0129-167X
- Publication type
Article
- DOI
10.1142/S0129167X13501085