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<p>We show that there exists a <i>q</i>-convex function in a neighborhood of a compact set <i>K</i> in a complex manifold <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathcal {M}\)</EquationSource> </InlineEquation> if and only if the <i>q</i>-nucleus of this compact set is empty. The latter can be characterized as the maximal <i>q</i>-pseudoconcave subset of <i>K</i>, i.e., a subset of <i>K</i> containing all other compact <i>q</i>-pseudoconcave subsets in <i>K</i>.</p>

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On compact sets possessing q-convex functions

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年10月14日

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  • Thomas Pawlaschyk,
  • Nikolay Shcherbina

摘要

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.