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Combinatorial Yamabe flow on hyperbolic bordered surfaces

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arxiv 2204.08191 v1 pith:4DW2QLOI submitted 2022-04-18 math.DG math.GT

classification math.DGmath.GT
keywords flowhyperbolicborderedcombinatorialsurfacesyamabealgorithmboundary
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This paper studies the combinatorial Yamabe flow on hyperbolic bordered surfaces. We show that the flow exists for all time and converges exponentially fast to conformal factor which produces a hyperbolic surface whose lengths of boundary components are equal to prescribed positive numbers. This provides an algorithm to such problems.

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Cited by 1 Pith paper

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  1. Discrete conformal structures on surfaces with boundary (III) -- Deformation

    math.DG 2025-07 conditional novelty 5.0 of 10

    Combinatorial Ricci and Calabi flows on discrete conformal structures over surfaces with boundary are proven to converge exponentially to prescribed boundary lengths, globally for two structure classes and locally for...

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