3 citations · 5 across the 5 of their papers we have counts for
7 papers
Rigidity of Koebe Polyhedra and Inversive Distance Circle Packings
John C. Bowers, Philip L. Bowers, Carl O. R. Lutz
Hyperbolic inversive distance circle packings on the -sphere correspond to Koebe polyhedra in the Beltrami-Klein model of hyperbolic -space. Koebe polyhedra…
Infinite circle packings on surfaces with conical singularities
Philip L. Bowers, Lorenzo Ruffoni
We show that given an infinite triangulation of a surface with punctures (i.e., with no vertices at the punctures) and a set of target cone angles smaller than at the punct…
Tame and relatively elliptic -structures on the thrice-punctured sphere
Samuel A. Ballas, Philip L. Bowers, Alex Casella +1
Suppose a relatively elliptic representation of the fundamental group of the thrice-punctured sphere is given. We prove that all projective structures on with holonomy…
Combinatorics encoding geometry: the legacy of Bill Thurston in the story of one theorem
Philip L. Bowers
This article presents a whirlwind tour of some results surrounding the Koebe-Andre'ev-Thurston Theorem, Bill Thurston's seminal circle packing theorem that appears in Chapter 13 of…
Almost all circle polyhedra are rigid
John C. Bowers, Philip L. Bowers, Kevin Pratt
We verify the infinitesimal inversive rigidity of almost all triangulated circle polyhedra in the Euclidean plane , as well as the infinitesimal inversive rigidity…
Rigidity of Circle Polyhedra in the 2-Sphere and of Hyperideal Polyhedra in Hyperbolic 3-Space
John C. Bowers, Philip L. Bowers, Kevin Pratt
We generalize Cauchy's celebrated theorem on the global rigidity of convex polyhedra in Euclidean -space to the context of circle polyhedra in the -sphere $\…
Ma-Schlenker c-Octahedra in the 2-Sphere
John C. Bowers, Philip L. Bowers
We present constructions inspired by the Ma-Schlenker example of~\cite{Ma:2012hl} that show the non-rigidity of spherical inversive distance circle packings. In contrast to the use…