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Polynomial hulls and analytic discs


Author: Egmont Porten
Journal: Proc. Amer. Math. Soc.
MSC (2010): Primary 32E20, 32H02, 32T05
DOI: https://doi.org/10.1090/proc/13596
Published electronically: June 22, 2017
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Abstract: The goal of the present note is to construct a class of examples for connected compact sets $ K\subset \mathbb{C}^n$ whose polynomial hull $ \widehat {K}$ cannot be covered by analytic discs with boundaries contained in an arbitrarily small neighborhood of $ K$. This gives an answer to a recent question raised by B. Drinovec Drnovšek and F. Forstnerič.


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Additional Information

Egmont Porten
Affiliation: Department of Mathematics, Mid Sweden University, Sundsvall, Sweden — and — Instytut Matematyki, Uniwersytet Jana Kochanowskiego w Kielcach, Kielce, Poland
Email: Egmont.Porten@miun.se

DOI: https://doi.org/10.1090/proc/13596
Received by editor(s): June 6, 2016
Received by editor(s) in revised form: November 14, 2016
Published electronically: June 22, 2017
Communicated by: Franc Forstneric
Article copyright: © Copyright 2017 American Mathematical Society