English

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.

Keywords

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