The Isostatic Conjecture
Metric Geometry
2018-10-10 v3
Abstract
We show that a jammed packing of disks with generic radii, in a generic container, is such that the minimal number of contacts occurs and there is only one dimension of equilibrium stresses. We also point out some connections to packings with different radii and results in the theory of circle packings whose graph forms a triangulation of a given topological surface. We also point out a counterexample, due to F. Nazarov, to a previous conjecture that that triangulated packings with fixed numbers of disks with fixed numbers of disks for each radius claiming that such packings were the most dense.
Keywords
Cite
@article{arxiv.1702.08442,
title = {The Isostatic Conjecture},
author = {Robert Connelly and Steven J. Gortler and Evan Solomonides and Maria Yampolskaya},
journal= {arXiv preprint arXiv:1702.08442},
year = {2018}
}
Comments
This is an updated and cleaned up and improved version of previous submissions