On combinatorial Calabi flow with hyperbolic circle patterns - Ge, Huabin; Hua, Bobo (Advances in mathematics (New York. 1965), 2018)
In this paper, we prove the long time existence of the combinatorial Calabi flow in hyperbolic background geometry and the convergence of the flow to a smooth hyperbolic surface under Thurston's combinatorial condition in full generality, which improves the result in [14]. This flow provides a natural algorithm to find Thurston's hyperbolic circle patterns.