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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2510.11943 |
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| _version_ | 1866915552989020160 |
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| author | Arosio, Leandro Kalm, Håkan Samuelsson Wold, Erlend F. |
| author_facet | Arosio, Leandro Kalm, Håkan Samuelsson Wold, Erlend F. |
| contents | We show that if $X$ is a totally real $d$-dimensional manifold attached to a polynomially convex compact set $K$ in $\mathbb{C}^n$, $d<n$, then there are arbitrarily small perturbations $X'$ of $X$ such that $K\cup X'$ is polynomially convex. The perturbations are induced by diffeomorphisms of $\mathbb{C}^n$ fixing $K$, which are $\bar\partial$-flat on $K\cup X$, and which are arbitrarily $C^k$-close to the identity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_11943 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Polynomial convexity of $\bar\partial$-flat perturbations of totally real sets Arosio, Leandro Kalm, Håkan Samuelsson Wold, Erlend F. Complex Variables We show that if $X$ is a totally real $d$-dimensional manifold attached to a polynomially convex compact set $K$ in $\mathbb{C}^n$, $d<n$, then there are arbitrarily small perturbations $X'$ of $X$ such that $K\cup X'$ is polynomially convex. The perturbations are induced by diffeomorphisms of $\mathbb{C}^n$ fixing $K$, which are $\bar\partial$-flat on $K\cup X$, and which are arbitrarily $C^k$-close to the identity. |
| title | Polynomial convexity of $\bar\partial$-flat perturbations of totally real sets |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2510.11943 |