In this talk I will describe how constant Gaussian curvature (CGC) surfaces interpolate the structures of the pleated boundary of the convex core and of the boundary at infinity of a quasi-Fuchsian manifold, and I will present a series of consequences of this phenomenon, such as a description of the renormalized volume in terms of the CGC surfaces foliations, and a generalization of McMullen's Kleinian reciprocity theorem.