Some Observations Concerning Polynomial Convexity

  • Sushil GoraiEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 302)


In this paper we discuss a couple of observations related to polynomial convexity. More precisely,
  1. (i)

    We observe that the union of finitely many disjoint closed balls with centres in \(\bigcup _{\theta \in [0,\pi /2]}e^{i\theta }V\) is polynomially convex, where V is a Lagrangian subspace of \(\mathbb {C}^n\).

  2. (ii)

    We show that any compact subset K of \(\{(z,w)\in \mathbb {C}^2:q(w)=\overline{p(z)}\}\), where p and q are two non-constant holomorphic polynomials in one variable, is polynomially convex and \(\mathcal {P}(K)=\mathcal {C}(K)\).



Polynomial convexity Closed ball Totally real Lagrangians 

2010 Mathematics Subject Classification

Primary: 32E20 



I would like to thank the referee for valuable comments. I would also like to thank Professor Peter de Paepe for pointing out a mistake in the earlier version of Corollary  4.1.


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© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsIndian Institute of Science Education and Research KolkataNadiaIndia

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