On polynomial convexity of compact subsets of totally-real submanifolds in [formula omitted

Abstract

Let K be a compact subset of a totally-real manifold M, where M is either a C2-smooth graph in C2n over Cn, or M=u−1{0} for a C2-smooth submersion u from Cn to R2n−k, k≤n. In this case we show that K is polynomially convex if and only if for a fixed neighbourhood U, defined in terms of the defining functions of M, there exists a plurisubharmonic function Ψ on Cn such that K⊂{Ψ<0}⊂U.