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

The purpose of this article is twofold. The first aim is to prove that if there exist a sequence $\{{\phi }_j\}\subset \mathrm{A}\mathrm{u}\mathrm{t}(\mathrm{\Omega })$ and $a\in \mathrm{\Omega }$ such that ${\lim }_{j\to \mathrm{\infty }}{\phi }_j(a)={\xi }_0$ and ${\lim }_{j\to \mathrm{\infty }}{\sigma }_{\mathrm{\Omega }}({\phi }_j(a))=1$, 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.