Presence or absence of analytic structure in maximal ideal spaces
  We study extensions of Wermer's maximality theorem to several complex variables. We exhibit various smoothly embedded manifolds in complex Euclidean space whose hulls are non-trivial but contain no analytic disks. We answer a question posed by Lee Stout concerning the existence of analytic structure for a uniform algebra whose maximal ideal space is a manifold. 
Alexander J. Izzo, H{\aa}kan Samuelsson Kalm, Erlend Forn{\ae}ss Wold
math.CV