Hulls of Surfaces

Abstract

In this paper it is shown that every compact two-dimensional manifold $S$, with or without boundary, can be embedded in ${\mathbb{C}}^3$ as a smooth submanifold $\Sigma$ in such a way that the polynomially convex hull of $\Sigma$, though strictly larger than $\Sigma$, contains no analytic disc.

arXiv commentAn additional open question, concerning rational convexity, along with a partial solution, was added at the end of the paper. Also, one misleading statement in the proof of the main theorem was clarified