On polynomial convexity of compact subsets of totally-real submanifolds in

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• 作者：Sushil Gorai ^{sushil.gorai@iiserkol.ac.in}
• 关键词：Polynomial convexity ; Totally real ; Plurisubharmonic functions
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：15 April 2017
• 年：2017
• 卷：448
• 期：2
• 页码：1305-1317
• 全文大小：360 K
• 卷排序：448

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.