Cheng and Yau showed that the Ricci curvature assumption in the Omori-Yau maximum principle can be replaced by the assumption of the existence of smooth cutoff functions of certain controllable geometry. Using this as the primary tool to extend some of Yau's work in proving the Calabi conjecture, they were able to construct complex-geometric analogues to the Poincaré ball model of hyperbolic space. In particular, they showed that complete Kähler-Einstein metrics of negative scalar curvature exist on any bounded, smooth, and strictly pseudoconvex subset of a finite-dimensional complex vector space.