文摘
Let K be a compact subset of a totally-real manifold M, where M is either a C2C2-smooth graph in C2nC2n over CnCn, or M=u−1{0}M=u−1{0} for a C2C2-smooth submersion u from CnCn to R2n−kR2n−k, k≤nk≤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 CnCn such that K⊂{Ψ<0}⊂UK⊂{Ψ<0}⊂U.