Approximation of biholomorphic maps between Runge domains by holomorphic automorphisms

2025/05/21 by Franc Forstnerič, Forstneric, Franc
Mathematics · #32M17 #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Meromorphic and Entire Functions #Primary 32E30. Secondary 14R10

paper · doi:10.48550/arxiv.2505.15129

openalex publication_date 2025/05/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that biholomorphic maps between certain pairs of Runge domains in the complex affine space \mathbb Cⁿ, n>1, are limits of holomorphic automorphisms of \mathbb Cⁿ. A similar result holds for volume preserving maps and also in Stein manifolds with the density property. This generalizes several results in the literature and provides a considerably simpler proof.

Citations

• Solving the Loewner PDE in complete hyperbolic starlike domains of \C^N

Related

• Carleman approximation by holomorphic automorphisms of \mathbb Cⁿ
• Characterization of \bf Cⁿ by its automorphism group
• Holomorphic mappings between domains in \mbb C²
• Approximations on certain domains of ℂⁿ
• Maps conjugating holomorphic maps in Cⁿ