#### Vol. 297, No. 1, 2018

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

### John Erik Fornæss and Erlend Fornæss Wold

Vol. 297 (2018), No. 1, 79–86
##### Abstract

In recent work by Zimmer it was proved that if $\Omega \subset {ℂ}^{n}$ is a bounded convex domain with ${C}^{\infty }$-smooth boundary, then $\Omega$ is strictly pseudoconvex provided that the squeezing function approaches 1 as one approaches the boundary. We show that this result fails if $\Omega$ is only assumed to be ${C}^{2}$-smooth.

##### Keywords
squeezing function, holomorphic embeddings, holomorphic mappings
##### Mathematical Subject Classification 2010
Primary: 32F45, 32H02