On compact sets possessing $q$-convex functions
Complex Variables
2025-06-02 v1
Abstract
We show that there exists a -convex function in a neighborhood of a compact set in a complex manifold if and only if the -nucleus of this compact set is empty. The latter can be characterized as the maximal -pseudoconcave subset of , i.e., a subset of containing all other compact -pseudoconcave subsets in .
Keywords
Cite
@article{arxiv.2505.24588,
title = {On compact sets possessing $q$-convex functions},
author = {Thomas Pawlaschyk and Nikolay Shcherbina},
journal= {arXiv preprint arXiv:2505.24588},
year = {2025}
}