https://neckpinch.com/authors/xinrong-zhao/New arXiv papers by Xinrong Zhao, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2601.15174/arxiv:2601.15174Wed, 21 Jan 2026 00:00:00 GMTXinrong Zhao — In this paper, we study a combinatorial Ricci flow on closed pseudo 3-manifolds (M,𝓣). We prove that if every edge in the triangulation 𝓣 has valence at least 9, then the combinatorial Ricci flow converges exponentially fast to the unique zero-curvature hyper-ideal metric. As a consequence, for any compact 3-manifold N with boundary admitting an ideal triangulation 𝓣_N whose edges all have valence at least 9, there exists a unique complete hyperbolic metric with totally geodesic boundary on N such that 𝓣_N is isotopic to a geometric decomposition of N. This provides a partial solution to the conjecture of Costantino, Frigerio, Martelli and Petronio, and hence an affirmative answer to Thurston's geometric ideal triangulation conjecture for such manifolds. Moreover, we obtain explicit upper and lower bounds for the resulting hyperbolic metric.Ricci flowGeometrizationBoundaries & non-compactLong-time existence & convergenceDiscrete & graph Ricci https://neckpinch.com/papers/2505.20091/arxiv:2505.20091Mon, 26 May 2025 00:00:00 GMTXinrong Zhao, Puchun Zhou — In this paper, we investigate the prescribed total geodesic curvature problem for generalized circle packing metrics in hyperbolic background geometry on surfaces with infinite cellular decompositions. To address this problem, we introduce a prescribed curvature flow-a discrete analogue of the Ricci flow on noncompact surfaces-specifically adapted to the setting of infinite cellular decompositions. We establish the well-posedness of the flow and prove two convergence results under certain conditions. Our approach resolves the prescribed total geodesic curvature problem for a broad class of surfaces with infinite cellular decompositions, yielding, in certain cases, smooth hyperbolic surfaces of infinite topological type with geodesic boundaries or cusps. Moreover, the proposed flow provides a method for constructing hyperbolic metrics from appropriate initial data.Ricci flowOther curvature flowsSurfacesBoundaries & non-compactDiscrete & graph Ricci