On compact sets possessing $q$-convex functions
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908386116763648 |
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| author | Pawlaschyk, Thomas Shcherbina, Nikolay |
| author_facet | Pawlaschyk, Thomas Shcherbina, Nikolay |
| contents | We show that there exists a $q$-convex function in a neighborhood of a compact set $K$ in a complex manifold $\mathcal{M}$ if and only if the $q$-nucleus of this compact set is empty. The latter can be characterized as the maximal $q$-pseudoconcave subset of $K$, i.e., a subset of $K$ containing all other compact $q$-pseudoconcave subsets in $K$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_24588 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On compact sets possessing $q$-convex functions Pawlaschyk, Thomas Shcherbina, Nikolay Complex Variables 32U05, 32F10, 32Q99 We show that there exists a $q$-convex function in a neighborhood of a compact set $K$ in a complex manifold $\mathcal{M}$ if and only if the $q$-nucleus of this compact set is empty. The latter can be characterized as the maximal $q$-pseudoconcave subset of $K$, i.e., a subset of $K$ containing all other compact $q$-pseudoconcave subsets in $K$. |
| title | On compact sets possessing $q$-convex functions |
| topic | Complex Variables 32U05, 32F10, 32Q99 |
| url | https://arxiv.org/abs/2505.24588 |