On the boundary behaviour of the squeezing function near linearly convex boundary points

Abstract

The purpose of this article is twofold. The first aim is to prove that if there exist a sequence $\{{\phi }_j\}\subset \mathrm{Aut}(\Omega )$ and $a\in \Omega$ such that ${\lim }_{j\to \infty }{\phi }_j(a)={\xi }_0$ and ${\lim }_{j\to \infty }{\sigma }_{\Omega }({\phi }_j(a))=1$, where ${\xi }_0$ is a linearly convex boundary point of finite type, then ${\xi }_0$ must be strongly pseudoconvex. Then, the second aim is to investigate the boundary behaviour of the squeezing function of a general ellipsoid.

10 pages