The Koebe-Andreev-Thurston theorem states that for any triangulation of a closed orientable surface Σg of genus g which is covered by a simple graph in the universal cover, there exists a unique metric of curvature 1,0 or −1 on the surface depending on whether g = 0,1 or ≥ 2 such that the surface with this metric admits a circle packing with combinatorics given by the triangulation. Furthermore, the circle packing is essentially rigid, that is, unique up to conformal automorphisms of the surface isotopic to the identity.
¶ In this paper, we consider projective structures on the surface where circle packings are also defined. We show that the space of projective structures on a surface of genus g ≥ 2 which admits a circle packing contains a neigborhood of the Koebe-Andreev-Thurston structure homeomorphic to ℝ6g−6. We furthemore show that if a circle packing consists of one circle, then the space is globally homeomorphic to ℝ6g−6 and that the circle packing is rigid.