English

On compact sets possessing $q$-convex functions

Complex Variables 2025-06-02 v1

Abstract

We show that there exists a qq-convex function in a neighborhood of a compact set KK in a complex manifold M\mathcal{M} if and only if the qq-nucleus of this compact set is empty. The latter can be characterized as the maximal qq-pseudoconcave subset of KK, i.e., a subset of KK containing all other compact qq-pseudoconcave subsets in KK.

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}
}
R2 v1 2026-07-01T02:50:38.047Z