Foliations of continuous q-pseudoconcave graphs

2020/04/03 by Thomas Pawlaschyk, Pawlaschyk, Thomas, Nikolay Shcherbina +1 · 3 citations
Mathematics · #Geometric and Algebraic Topology #Geometric Analysis and Curvature Flows #Point processes and geometric inequalities

paper · doi:10.48550/arxiv.2004.01797

Abstract

We show that for k = 0, 1 the graph of a continuous mapping f:D → ℝ^k×ℂ^p, defined on a domain D in ℂⁿ×ℝ^k, is locally foliated by complex n-dimensional submanifolds if and only if its complement is n-pseudoconvex (in the sense of Rothstein) relatively to (D×ℝ^k)×ℂ^p⊂ ℂⁿ×ℂ^k×ℂ^p.

Cited by

• On rigid q-plurisubharmonic functions and q-pseudoconvex tube domains in ℂⁿ
• On compact sets possessing q-convex functions
• Analytic structure of q-pseudoconcave subsets of continuous graphs

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