On the Deformation of Thurston’s Circle Packings with Obtuse Intersection Angles

We study Thurston’s circle packings with obtuse intersection angles on closed surfaces. By using combinatorial Ricci/Calabi flows and variational principle, we extend Thurston’s existence theorem for circle packings with non-obtuse intersection angles to those with obtuse intersection angles. As consequences, we generalize the existence and convergence results related to Chow-Luo’s combinatorial Ricci flows (J Differ Geom 63(1):97–129, 2018) and Ge’s combinatorial Calabi flows (Combinatorial Methods and Geometric Equations, Thesis (Ph.D.), Peking University, Beijing, 2012, Trans Am math Soc 370(2):1377–1391, 2018, Adv Math 333:528–533, 2018).