A non-strictly pseudoconvex domain for which the squeezing function   tends to one towards the boundary
  In recent work by Zimmer it was proved that if $\Omega\subset\mathbb C^n$ is a bounded convex domain with $C^\infty$-smooth boundary, then $\Omega$ is strictly pseudoconvex provided that the squeezing function approaches one as one approaches the boundary. We show that this result fails if $\Omega$ is only assumed to be $C^2$-smooth. 
John Erik Forn{\ae}ss and Erlend Forn{\ae}ss Wold
math.CV