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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.04967 |
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| _version_ | 1866917368233459712 |
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| author | Valnegri, Filippo |
| author_facet | Valnegri, Filippo |
| contents | Let $Z\subset\mathbb{C}^N$ be an $n$-pseudoconcave subset, for $1\leq n<N$, which is locally the graph of a continuous function over a closed subset of $\mathbb{C}^n\times\mathbb{R}$. We show that $Z$ can be realised as the disjoint union of $n$-dimensional complex manifolds. In particular, the same conclusion can be made for any $n$-pseudoconcave subset $Z$ of the graph $Γ(g)$ of a continuous function $g:D\subset\mathbb{C}^n\times\mathbb{R}\to\mathbb{R}\times\mathbb{C}^p$, for $n\geq 1$ and $p\geq 0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_04967 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Analytic structure of $q$-pseudoconcave subsets of continuous graphs Valnegri, Filippo Complex Variables Let $Z\subset\mathbb{C}^N$ be an $n$-pseudoconcave subset, for $1\leq n<N$, which is locally the graph of a continuous function over a closed subset of $\mathbb{C}^n\times\mathbb{R}$. We show that $Z$ can be realised as the disjoint union of $n$-dimensional complex manifolds. In particular, the same conclusion can be made for any $n$-pseudoconcave subset $Z$ of the graph $Γ(g)$ of a continuous function $g:D\subset\mathbb{C}^n\times\mathbb{R}\to\mathbb{R}\times\mathbb{C}^p$, for $n\geq 1$ and $p\geq 0$. |
| title | Analytic structure of $q$-pseudoconcave subsets of continuous graphs |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2603.04967 |