Xiaoxiao Zhang — Neckpinchhttps://neckpinch.com/authors/xiaoxiao-zhang/New arXiv papers by Xiaoxiao Zhang, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT Combinatorial Calabi flows with ideal circle patternshttps://neckpinch.com/papers/2501.01605/arxiv:2501.01605Fri, 03 Jan 2025 00:00:00 GMTXiaoxiao Zhang — In this paper, we extend the work of Ge-Hua-Zhou on combinatorial Ricci flows for ideal circle patterns to combinatorial Calabi flows in both hyperbolic and Euclidean background geometry. We prove the solution to the combinatorial Calabi flows with any given initial Euclidean (hyperbolic resp.)ideal circle pattern exists for all time and converges exponentially fast to a flat cone metric (hyperbolic resp.) on a given surface.Ricci flowOther curvature flowsKähler geometryLong-time existence & convergenceDiscrete & graph Ricci