Work

Approximation of biholomorphic maps between Runge domains by holomorphic automorphisms

Year: 2025

Type: article

Abstract: We show that biholomorphic maps between certain pairs of Runge domains in the complex affine space $${\mathbb {C} }^n$$ C n , $$n>1$$ n > 1 , are limits of holomorphic automorphisms of $${\mathbb {C} }^n$$ C n . A similar result holds for volume preserving maps and also in Stein manifolds with the density property. This generalises several results in the literature with considerably simpler proofs.

Source: Complex Analysis and its Synergies

DOI: 10.1007/s40627-025-00163-3

Author: Franc Forstnerič

Institutions: University of Ljubljana, Institute of Mathematics, Physics, and Mechanics

Language: English

Topic: Holomorphic and Operator Theory

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,990

Funders: European Commission, Javna Agencija za Raziskovalno Dejavnost RS