Some results on the convexity of the closure of the domain of a   maximally monotone operator
  We provide a concise analysis about what is known regarding when the closure of the domain of a maximally monotone operator on an arbitrary real Banach space is convex. In doing so, we also provide an affirmative answer to a problem posed by Simons. 
Jonathan M. Borwein and Liangjin Yao
math.FA