Non-rigidity of spherical inversive distance circle packings
Jiming Ma, Jean-Marc Schlenker
TL;DR
This paper presents a counterexample showing that spherical inversive distance circle packings are not uniquely determined by their inversive distances, challenging previous assumptions in the field.
Contribution
It provides the first known counterexample to Bowers-Stephenson's conjecture in the spherical setting, demonstrating non-rigidity.
Findings
Counterexample disproves the conjecture
Spherical inversive distance circle packings are not rigid
Inversive distances do not uniquely determine packings
Abstract
We give a counterexample of Bowers-Stephenson's conjecture in the spherical case: spherical inversive distance circle packings are not determined by their inversive distances.
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Taxonomy
TopicsPoint processes and geometric inequalities · Geometric and Algebraic Topology · Quasicrystal Structures and Properties