A Cantor set whose polynomial hull contains no analytic discs

Alexander J. Izzo; Norman Levenberg

A Cantor set whose polynomial hull contains no analytic discs

Complex Variables 2019-03-04 v3

Authors: Alexander J. Izzo , Norman Levenberg

Abstract

A generalization of a result of Wermer concerning the existence of polynomial hulls without analytic discs is presented. As a consequence it is shown that there exists a Cantor set $X$ in ${\mathbb C}^3$ whose polynomial hull is strictly larger than $X$ but contains no analytic discs.

Cite

@article{arxiv.1801.03205,
  title  = {A Cantor set whose polynomial hull contains no analytic discs},
  author = {Alexander J. Izzo and Norman Levenberg},
  journal= {arXiv preprint arXiv:1801.03205},
  year   = {2019}
}

Comments

The paper has been almost completely rewritten. A much shorter, but less direct, proof is given that yields a stronger result

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