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Circle packings and hyperbolic surfaces of finite type
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This paper constructs hyperbolic polyhedral metrics via circle packings. We introduce the curvature of circles as a parameter to include all three types of constant curvature curves in the hyperbolic geometry. This provides a unified approach to producing polyhedral metrics for surfaces of broader topological types. The combinatorial total geodesic curvature serves as an effective tool for establishing the existence and uniqueness of the packing.
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Cited by 1 Pith paper
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A prescribed curvature flow on hyperbolic surfaces with infinite topological type
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.
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