Proves existence, rigidity, and uniformization for infinite regular circle patterns with 0≤Θ<π and for infinite trivalent hyperbolic polyhedra.
Zhou,Circle patterns with obtuse exterior intersection angles
2 Pith papers cite this work. Polarity classification is still indexing.
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The Circle Pattern Theorem extends to quasi-simplicial triangulations of closed surfaces, with curvature images characterized by KAT inequalities on all subsets of lifted vertices.
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Characterizations of infinite circle patterns and convex polyhedra in hyperbolic 3-space
Proves existence, rigidity, and uniformization for infinite regular circle patterns with 0≤Θ<π and for infinite trivalent hyperbolic polyhedra.
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Circle Pattern Theorem for Quasi-simplicial Triangulated Surfaces
The Circle Pattern Theorem extends to quasi-simplicial triangulations of closed surfaces, with curvature images characterized by KAT inequalities on all subsets of lifted vertices.