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Combinatorial Ricci flows on infinite disk triangulations

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arxiv 2504.05817 v1 pith:PCP7TL4A submitted 2025-04-08 math.GT math.DG

Huabin Ge , Bobo Hua , Puchun Zhou This is my paper · ORCID
classification math.GTmath.DG
keywords crfsinfinitetriangulationsbackgrounddiskflowshyperbolicresults
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In this paper, we introduce combinatorial Ricci flows (CRFs in short) in Euclidean and hyperbolic background geometries on infinite triangulations of the open disk, which are discrete analogs of Ricci flows on simply connected open surfaces. We establish well-posedness results, the existence and the uniqueness, of CRFs in both Euclidean and hyperbolic background geometries. Moreover, we prove convergence results of CRFs, which indicate a uniformization theorem for CRFs on infinite disk triangulations. As an application, we prove an existence result of circle-packing metrics with infinite prescribed cone angles in hyperbolic background geometry. To our knowledge, these are the first results of CRFs on infinite triangulations.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. A prescribed curvature flow on hyperbolic surfaces with infinite topological type

    math.GT 2025-05 conditional novelty 7.0 of 10

    An infinite version of the prescribed curvature flow is shown to converge under side conditions, yielding generalized circle packings and smooth infinite-type hyperbolic surfaces with prescribed total geodesic curvature.

  2. Infinite Combinatorial Yamabe Flows in Three Dimensions

    math.DG 2026-07 accept novelty 6.0 of 10

    Under bounded degree and non-degeneracy, original 3D combinatorial Yamabe flows on infinite triangulations exist uniquely for short time; extended solid-angle flows exist globally.

  3. The existence and uniqueness of infinite combinatorial Yamabe flows

    math.DG 2025-07 conditional novelty 6.0 of 10

    The infinite combinatorial Yamabe flow exists locally and uniquely on uniformly nondegenerate, uniformly Delaunay triangulations with bounded degree, has a globally defined extension, and converges near the regular me...

  4. Characterization of Infinite Ideal Polyhedra in Hyperbolic 3-Space via Combinatorial Ricci Flow

    math.GT 2025-06 reject novelty 6.0 of 10

    This paper proves new convergence results for infinite combinatorial Ricci flow on ideal circle patterns, but the claimed existence of infinite ideal hyperbolic polyhedra is not yet established.

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