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

Abstract

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.

References in corpus (2)

• Boundary behavior of the squeezing functions of $\mathbb{C}$-convex domains and plane domains
• A characterization of the ball

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• On boundary points at which the squeezing function tends to one
• Asymptotic strictly pseudoconvex CR structure for asymptotically locally complex hyperbolic manifolds
• Characterizing strong pseudoconvexity, obstructions to biholomorphisms, and Lyapunov exponents
• Fridman's invariant, squeezing functions, and exhausting domains
• Some properties of $h$-extendible domains in ${\mathbb{C}}^{n+1}$
• A comparison of two biholomorphic invariants