A Hull with No Nontrivial Gleason Parts
  The existence of a nontrivial polynomially convex hull with every point a one-point Gleason part and with no nonzero bounded point derivations is established. This strengthens the \hbox{celebrated} result of Stolzenberg that there exists a nontrivial polynomially convex hull that contains no analytic discs. A doubly generated counterexample to the peak point conjecture is also presented. 
Brian J. Cole, Swarup N. Ghosh, and Alexander J. Izzo
math.CV