A new proof of Bowers-Stephenson conjecture

Abstract

Inversive distance circle packing on surfaces was introduced by Bowers-Stephenson as a generalization of Thurston's circle packing and conjectured to be rigid. The infinitesimal and global rigidity of circle packing with nonnegative inversive distance were proved by Guo and Luo respectively. The author proved the global rigidity of circle packing with inversive distance in $(-1,+\infty )$. In this paper, we give a new variational proof of the Bowers-Stephenson conjecture for inversive distance in $(-1,+\infty )$, which simplifies the existing proofs and could be generalized to three dimensional case.

19 pages

References in corpus (5)

• Rigidity of Polyhedral Surfaces
• Geometric triangulations and discrete Laplacians on manifolds
• On the deformation of inversive distance circle packings, II
• Circle patterns with obtuse exterior intersection angles
• On the deformation of ball packings

Cited by in corpus (3)

• Rigidity of discrete conformal structures on surfaces
• Fractional combinatorial Calabi flow on surfaces
• Combinatorial Ricci flow on cusped 3-manifolds