Approximation of biholomorphic maps between Runge domains by holomorphic automorphisms

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2025年8月25日

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Franc Forstnerič

摘要

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.