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In recent work by Zimmer it was proved that if $\Omega\subset\mathbb C^n$ isa bounded convex domain with $C^\infty$-smooth boundary, then $\Omega$ isstrictly pseudoconvex provided that the squeezing function approaches one asone approaches the boundary. We show that this result fails if $\Omega$ is onlyassumed to be $C^2$-smooth.

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