A geometric inequality for circle packings

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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.
11 pages, submitted

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Algebraic Geometry, Optimization and Control

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http://salesiana.dossiersoluciones.com/handle/123456789/64160

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0205278
 http://arxiv.org/abs/math/0205278
 Discrete and Computational Geometry, Vol. 31, No. 3, 2004.
 doi:10.1007/s00454-003-2880-2

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arXiv