A non-strictly pseudoconvex domain for which the squeezing function tends to 1 towards the boundary

In recent work by Zimmer it was proved that if Ω ⊂ C n is a bounded convex domain with C ∞-smooth boundary, then Ω is strictly pseudoconvex provided that the squeezing function approaches one as one approaches the boundary. We show that this result fails if Ω is only assumed to be C 2 –smooth.