Notes on the roots of Steiner polynomials

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We study the location and the size of the roots of Steiner polynomials of convex bodies in the Minkowski relative geometry. Based on a problem of Teissier on the intersection numbers of Cartier divisors of compact algebraic varieties it was conjectured that these roots have certain geometric properties related to the in- and circumradius of the convex body. We show that the roots of 1-tangential bodies fulfill the conjecture, but we also present convex bodies violating each of the conjectured properties.

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Metric Geometry, 52A20 (Primary); 52A39, 30C15 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/125609

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0703373
 http://arxiv.org/abs/math/0703373

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arXiv