Foliations of continuous q-pseudoconcave graphs
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2020
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| _version_ | 1866916998650265600 |
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| author | Pawlaschyk, Thomas Shcherbina, Nikolay |
| author_facet | Pawlaschyk, Thomas Shcherbina, Nikolay |
| contents | We show that for $k = 0, 1$ the graph of a continuous mapping $f:D \to \mathbb{R}^k\times\mathbb{C}^p$, defined on a domain $D$ in $\mathbb{C}^n\times\mathbb{R}^k$, is locally foliated by complex $n$-dimensional submanifolds if and only if its complement is $n$-pseudoconvex (in the sense of Rothstein) relatively to $(D\times\mathbb{R}^k)\times\mathbb{C}^p\subset \mathbb{C}^{n}\times\mathbb{C}^k\times\mathbb{C}^p$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2004_01797 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Foliations of continuous q-pseudoconcave graphs Pawlaschyk, Thomas Shcherbina, Nikolay Complex Variables 32F10, 32D20 (Primary), 37F75 (Secondary) We show that for $k = 0, 1$ the graph of a continuous mapping $f:D \to \mathbb{R}^k\times\mathbb{C}^p$, defined on a domain $D$ in $\mathbb{C}^n\times\mathbb{R}^k$, is locally foliated by complex $n$-dimensional submanifolds if and only if its complement is $n$-pseudoconvex (in the sense of Rothstein) relatively to $(D\times\mathbb{R}^k)\times\mathbb{C}^p\subset \mathbb{C}^{n}\times\mathbb{C}^k\times\mathbb{C}^p$. |
| title | Foliations of continuous q-pseudoconcave graphs |
| topic | Complex Variables 32F10, 32D20 (Primary), 37F75 (Secondary) |
| url | https://arxiv.org/abs/2004.01797 |