Circle patterns with obtuse exterior intersection angles

Abstract

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.

24 pages, 1 figure

References in corpus (2)

• Rigidity of Polyhedral Surfaces
• On the deformation of inversive distance circle packings, II

Cited by in corpus (7)

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• Combinatorial Calabi flow with surgery on surfaces
• Tame the flexibility of circle patterns