On polynomial convexity of compact subsets of totally-real submanifold\n in \ℂⁿ

2015/04/27 by Sushil Gorai, Gorai, Sushil
Mathematics · Physics and Astronomy · #32E20 #Advanced Differential Geometry Research #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1504.07049

openalex publication_date 2015/04/27 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

Let K be a compact subset of a totally-real manifold M, where M is\neither a \C²-smooth graph in \ℂ²ⁿ over \ℂⁿ,\nor M=u^-1 0 for a \C²-smooth submersion u from\n\ℂⁿ to \ℝ^2n-k, k\≤ n. In this case we show that K\nis polynomially convex if and only if for a fixed neighbourhood U, defined in\nterms of the defining functions of M, there exists a plurisubharmonic\nfunction \Ψ on \ℂⁿ such that K\⊂ \Ψ<0 \⊂ U.\n

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