Arkiv för Matematik

Volume 57 (2019)

Number 2

A Cantor set whose polynomial hull contains no analytic discs

Pages: 373 – 379



Alexander J. Izzo (Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, Ohio, U.S.A.)

Norman Levenberg (Department of Mathematics, Indiana University, Bloomington, In., U.S.A.)


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.

2010 Mathematics Subject Classification


Received 25 February 2019

Accepted 31 May 2019

Published 7 October 2019