Approximation of biholomorphic maps between Runge domains by holomorphic automorphisms
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910020702044160 |
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| author | Forstneric, Franc |
| author_facet | Forstneric, Franc |
| contents | We show that biholomorphic maps between certain pairs of Runge domains in the complex affine space $\mathbb C^n$, $n>1$, are limits of holomorphic automorphisms of $\mathbb C^n$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_15129 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Approximation of biholomorphic maps between Runge domains by holomorphic automorphisms Forstneric, Franc Complex Variables Primary 32E30. Secondary 14R10, 32M17 We show that biholomorphic maps between certain pairs of Runge domains in the complex affine space $\mathbb C^n$, $n>1$, are limits of holomorphic automorphisms of $\mathbb C^n$. 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. |
| title | Approximation of biholomorphic maps between Runge domains by holomorphic automorphisms |
| topic | Complex Variables Primary 32E30. Secondary 14R10, 32M17 |
| url | https://arxiv.org/abs/2505.15129 |