Geometry of bounded generic domains with piecewise smooth boundary

Abstract

In this paper, we study the geometry of bounded domains with piecewise smooth boundary. Specifically, we obtain the relationship between the squeezing function corresponding to polydisk and Levi flatness on bounded generic convex domains. As an application, we prove that a two dimensional bounded generic convex domain with piecewise $C^2$-smooth boundary that admits a finite volume quotient is biholomorphic to bidisk. Moreover, we show that any Teichm$\ddot{\operatorname{u}}$ller space $\mathcal{T}_g$ with $g\geq2$ can not be biholomorphic to a bounded generic domain with piecewise $C^2$-smooth boundary.