A geometric inequality for circle packings
Algebraic Geometry
2007-05-23 v1 Optimization and Control
Abstract
A geometric inequality among three triangles, originating in circle packing problems, is introduced. In order to prove it, we reduce the original formulation to the nonnegativity of a particular polynomial in four real indeterminates. Techniques based on sum of squares decompositions, semidefinite programming, and symmetry reduction are then applied to provide an easily verifiable nonnegativity certificate.
Cite
@article{arxiv.math/0205278,
title = {A geometric inequality for circle packings},
author = {Pablo A. Parrilo and Ronen Peretz},
journal= {arXiv preprint arXiv:math/0205278},
year = {2007}
}
Comments
11 pages, submitted