The authors prove existence and rigidity of infinite ideal polyhedra via a uniformization theorem for embedded ideal circle patterns whose type depends on both cellular structure and intersection angles.
Graphs with nonnegative curvature outside a finite subset, harmonic functions, and number of ends
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Infinite Ideal Polyhedra in Hyperbolic 3-Space: Existence and Rigidity
The authors prove existence and rigidity of infinite ideal polyhedra via a uniformization theorem for embedded ideal circle patterns whose type depends on both cellular structure and intersection angles.