https://neckpinch.com/authors/rongyuan-liu/New arXiv papers by Rongyuan Liu, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2505.24762/arxiv:2505.24762Fri, 30 May 2025 00:00:00 GMTWenjun Li, Rongyuan Liu, Guohao Chen, Aijin Lin — In this paper we introduce the branched α-flows on closed surfaces with Euler characteristic χ≤ 0. Based on the strict convexity of the branched α-potentials, we establish the long time existence and convergence of the solutions to the branched α-flows, which generalizes Ge and Xu's main results on the α-flows. In addtion, we study the prescribed curvature problems under the relaxed precondition χ(M)∈ ℤ via alternative α-flows, establishing admissibility conditions for prescribed curvatures and their exponential convergence to target metrics.Ricci flowSurfacesLong-time existence & convergenceDiscrete & graph Ricci