Properties of squeezing functions on $h$-extendible domains

The purpose of this article is twofold. First, we prove that the squeezing function approaches 1 near strongly pseudoconvex boundary points of bounded domains in ${\mathbb{C}}^{n+1}$. Second, we show that the squeezing function approaches 1 along certain sequences converging to pseudoconvex boundary points of finite type, including uniformly $\mathrm{\Lambda }$-tangential and spherically $\frac{1}{2m}$-tangential convergence patterns.