# A note on the boundary behaviour of the squeezing function and Fridman invariant

## TL;DR

This paper investigates the boundary behavior of the squeezing function and Fridman invariant in complex domains, showing that certain convergence properties imply strong pseudoconvexity at boundary points.

## Contribution

It establishes conditions under which the boundary point must be strongly pseudoconvex based on the limits of these invariants.

## Key findings

- If the squeezing function tends to 1, the boundary point is strongly pseudoconvex.
- If the Fridman invariant tends to 0, the boundary point is strongly pseudoconvex.
- Results apply to domains with smooth pseudoconvex boundaries of finite type and Levi form of corank at most 1.

## Abstract

Let $\Omega$ be a domain in $\mathbb C^n$. Suppose that $\partial\Omega$ is smooth pseudoconvex of D'Angelo finite type near a boundary point $\xi_0\in \partial\Omega$ and the Levi form has corank at most $1$ at $\xi_0$. Our goal is to show that if the squeezing function $s_\Omega(\eta_j)$ tends to $1$ or the Fridman invariant $h_\Omega(\eta_j)$ tends to $0$ for some sequence $\{\eta_j\}\subset \Omega$ converging to $\xi_0$, then this point must be strongly pseudoconvex.