Longtime existence and convergence conjecture for discrete conformal curvature flows with surgery

Let $(M,V,\varepsilon)$ be a closed connected weighted marked surface, where $\varepsilon:V\rightarrow\{0,1\}$. Consider an initial Euclidean or hyperbolic polyhedral metric induced by Glickenstein's discrete conformal structures on $(M,V,\varepsilon)$, and allow surgeries by flipping whenever needed to maintain the weighted Delaunay condition. Longtime existence and convergence conjecture. The combinatorial Ricci flow and the combinatorial Calabi flow with surgery exist for all time and converge exponentially fast. This conjecture concerns the global behavior of the two principal combinatorial curvature flows for Glickenstein's discrete conformal structures. It is supported by results for some special cases, but the general assertion for arbitrary closed connected weighted marked surfaces remains open.