Runge approximation on convex sets implies the Oka property

• 成果类型: Article
• 署名作者: Forstneric, Franc
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2006.163.689
• 发表日期: 2006
• 页码: 689-707
• 关键词: holomorphic submersions; algebraic-surfaces; PRINCIPLE; sections; mappings; EMBEDDINGS; MANIFOLDS; SPACES

摘要

We prove that the classical Oka property of a complex manifold Y, concerning the existence and homotopy classification of holomorphic mappings from Stein manifolds to Y, is equivalent to a Runge approximation property for holomorphic maps from compact convex sets in Euclidean spaces to Y.