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

TL;DR

This paper investigates the boundary behavior of the squeezing function near linearly convex boundary points, proving conditions under which such points are strongly pseudoconvex and analyzing the squeezing function on ellipsoids.

Contribution

It establishes that certain automorphism sequences imply strong pseudoconvexity at boundary points and explores the squeezing function's behavior on ellipsoids.

Findings

Linearly convex boundary points with specific automorphism sequences are strongly pseudoconvex.

The boundary behavior of the squeezing function is characterized for general ellipsoids.

Abstract

The purpose of this article is twofold. The first aim is to prove that if there exist a sequence $\{\varphi_j\}\subset \mathrm{Aut}(\Omega)$ and $a\in \Omega$ such that $\lim_{j\to\infty}\varphi_j(a)=\xi_0$ and $\lim_{j\to\infty}\sigma_\Omega(\varphi_j(a))=1$, 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.