  It is an old question how massive polynomial hulls of Cantor sets in
$\mathbb{C}^n$ can be. In contrast to expectation e.g. Rudin, Vitushkin and
Henkin showed on examples that it can be rather massive. Motivated by problems
of holomorphic convexity of subsets of strictly pseudoconvex boundaries and
removable singularities the question was asked for Cantor sets in the unit
sphere. It was known that tame Cantor sets in the unit sphere are polynomially
convex. We give an example of a wild Cantor set in the sphere whose polynomial
hull contains a large ball. In some sense this can be opposed to a still open
conjecture of Vitushkin on the existence of a lower bound for the diameter of
the largest boundary component of a relatively closed complex curve in the ball
passing through the origin.
