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Circle patterns with obtuse exterior intersection angles
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Thurston's Circle Pattern Theorem studies existence and rigidity of circle patterns of a given combinatorial type and the given non-obtuse exterior intersection angles. Using topological degree theory, variational principle, Teichmuller theory, and Sard's Theorem, this paper generalizes Circle Pattern Theorem to the case of obtuse exterior intersection angles.
Forward citations
Cited by 3 Pith papers
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Combinatorial Calabi flow for ideal circle pattern
The combinatorial Calabi flow for ideal circle patterns exists for all time and converges exponentially fast to the target ideal circle pattern metric whenever the target curvature vector is attainable.
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Combinatorial Calabi flows with ideal circle patterns
It extends combinatorial Calabi flow to ideal circle patterns in Euclidean and hyperbolic geometry, with global existence proved and exponential convergence claimed.
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Improved explicit estimates for the discrete Laplace operator with hyperbolic circle patterns
The paper gives explicit, radius-independent upper bounds for the coefficients of the discrete Laplacian on hyperbolic circle patterns for all weights in [0, π) satisfying a structural condition.
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