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

DOI: 10.2140/pjm.2018.297.79

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

Milestones

Received: 5 December 2016

Revised: 9 January 2018

Accepted: 9 January 2018

Published: 7 October 2018