On the uniform squeezing property of bounded convex domains in \(\mathbb{C}^n\) (Q265525)

Inspired by the works of \textit{K. Liu} et al. [J. Differ. Geom. 68, No. 3, 571--637 (2004; Zbl 1078.30038); J. Differ. Geom. 69, No. 1, 163--216 (2005; Zbl 1086.32011)] and \textit{S. Yeung} [Adv. Math. 221, No. 2, 547--569 (2009; Zbl 1165.32004)], \textit{F. Deng} et al. [Pac. J. Math. 257, No. 2, 319--341 (2012; Zbl 1254.32015)] introduced the concept of a ``squeezing function''. Since then, many authors have studied properties of squeezing functions and their applications.NEWLINENEWLINEIn the paper under review, the authors prove that the squeezing function for any bounded convex domain has a uniform lower bound. They also show that if the domain admits a \textit{spherically extreme} boundary point \(p\) in a neighborhood of which the boundary is \(C^2\)-smooth, then the squeezing function tends to 1 at \(p\). For the proof, the authors use the scaling method.