https://neckpinch.com/authors/yuerong-bian/New arXiv papers by Yuerong Bian, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2610.25745/arxiv:2610.25745Mon, 19 Oct 2026 00:00:00 GMTYuerong Bian, Xu Xu — We study the combinatorial Calabi flow associated with vertex scalings on infinitely triangulated surfaces with piecewise Euclidean and piecewise hyperbolic metrics. Under the assumptions of uniformly bounded vertex degree and an ε-uniformly nondegenerate initial metric, we establish short-time existence of smooth solutions and prove uniqueness among solutions that are continuous in the L^∞ norm.Other curvature flowsKähler geometryStability & uniquenessHarmonic maps & DeTurck trickDiscrete & graph Ricci https://neckpinch.com/papers/2607.25691/arxiv:2607.25691Tue, 28 Jul 2026 00:00:00 GMTYuerong Bian, Xu Xu — We study the combinatorial Yamabe flow on infinitely triangulated surfaces with piecewise hyperbolic metrics. Under the assumptions of uniformly bounded vertex degree and an ε-uniformly nondegenerate initial metric, we establish the short-time existence and uniqueness of smooth solutions to the combinatorial Yamabe flow. To address the potential degeneration of triangles along the evolution, we introduce an extended flow with generalized curvature, and establish the global existence of solutions to the extended flow.Furthermore, under an integrability condition, we establish the uniqueness of solutions to this extended flow, which follows from the stability property of the solutions. These results provide a local well-posedness theory for the hyperbolic combinatorial Yamabe flow on infinitely triangulated surfaces.Yamabe flowStability & uniquenessLong-time existence & convergenceHarmonic maps & DeTurck trickDiscrete & graph Ricci