On compact sets possessing q-convex functions

2025/05/30 by Pawlaschyk, Thomas, Shcherbina, Nikolay
#32F10 #32Q99 #32U05 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2505.24588

Abstract

We show that there exists a q-convex function in a neighborhood of a compact set K in a complex manifold 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.

Citations

• Foliations of continuous q-pseudoconcave graphs

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