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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:448

Article

Gorai, Sushil¹ 

[1] Indian Inst Sci Educ & Res Kolkata, Dept Math & Stat, Mohanpur 741246, India

关键词: Polynomial convexity;    Totally real;    Plurisubharmonic functions;   

DOI  :  10.1016/j.jmaa.2016.11.027

来源: Elsevier

【 摘 要 】

Let K be a compact subset of a totally-real manifold M, where M is either a C-2-smooth graph in C-2n over C-n, or M = u(-1){0} for a C-2-smooth submersion u from C-n 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 Psi on C-n such that K subset of {Psi < 0} subset of U. (C) 2016 Published by Elsevier Inc.

【 授权许可】

Free