Runge approximation on convex sets implies the Oka property

DOI10.4007/annals.2006.163.689zbMath1103.32004arXivmath/0402278OpenAlexW2034370106MaRDI QIDQ2500438

Franc Forstnerič

Publication date: 24 August 2006

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0402278

zbMATH Keywords

entire functionStein manifoldOka propertyholomorphic mappingRunge approximation

Mathematics Subject Classification ID

Stein manifolds (32Q28) Stein spaces (32E10) Topological aspects of complex manifolds (32Q55) Holomorphic, polynomial and rational approximation, and interpolation in several complex variables; Runge pairs (32E30)

Related Items (18)

Interpolation by conformal minimal surfaces and directed holomorphic curves ⋮ Oka manifolds ⋮ Gromov's Oka principle, fiber bundles and the conformal module ⋮ Oka manifolds: from Oka to Stein and back ⋮ Recent developments on Oka manifolds ⋮ Oka properties of complements of holomorphically convex sets ⋮ Approximation of holomorphic mappings on strongly pseudoconvex domains ⋮ The generalized Oka-Grauert principle for 1-convex manifolds ⋮ Holomorphic Approximation: The Legacy of Weierstrass, Runge, Oka–Weil, and Mergelyan ⋮ Riemann surfaces in Stein manifolds with the density property ⋮ A splitting lemma for coherent sheaves ⋮ Stein structures and holomorphic mappings ⋮ Acyclic embeddings of open Riemann surfaces into new examples of elliptic manifolds ⋮ Stein neighborhood bases of embedded strongly pseudoconvex domains and approximation of mappings ⋮ The Hartogs extension theorem for holomorphic vector bundles and sprays ⋮ A relative Oka-Grauert principle for holomorphic submersions over 1-convex spaces ⋮ Approximation of holomorphic maps with a lower bound on the rank ⋮ Holomorphic curves in complex spaces

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