A Cantor set whose polynomial hull contains no analytic discs

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.

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