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arXiv · 2505.24588

On compact sets possessing $q$-convex functions

Thomas Pawlaschyk·Nikolay Shcherbina
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Abstract

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 $K$.

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Thomas Pawlaschyk, Nikolay Shcherbina. 2025-05-30. On compact sets possessing $q$-convex functions. https://arxiv.org/abs/2505.24588

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