Inversive distance circle packing was introduced by Bowers and Stephenson, who conjectured the rigidity and existence of the inversive distance circle packing metrics. The rigidity conjecture for Euclidean and hyperbolic background geometry with nonnegative inversive distance was proved by Guo Ren and Luo Feng. In this talk, we will discuss some recent progress on the rigidity and deformation of inversive distance circle packing metrics. Part of the talk is based on the joint work with Huabin Ge.

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