Three-dimensional polyhedra can be described by three polynomial inequalities

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dc.creatorAverkov, Gennadiy
dc.creatorHenk, Martin
dc.date2008-07-14
dc.date.accessioned2026-07-07T09:50:10Z
dc.date.available2026-07-07T09:50:10Z
dc.descriptionBosse et al. conjectured that for every natural number $d \ge 2$ and every $d$-dimensional polytope $P$ in $\real^d$ there exist $d$ polynomials $p_0(x),...,p_{d-1}(x)$ satisfying $P=\{x \in \mathbb{R}^d : p_0(x) \ge 0, >..., p_{d-1}(x) \ge 0 \}.$ We show that for dimensions $d \le 3$ even every $d$-dimensional polyhedron can be described by $d$ polynomial inequalities. The proof of our result is constructive.
dc.description23 pages, 8 figures
dc.identifierhttps://arxiv.org/abs/0807.2137
dc.identifierhttp://arxiv.org/abs/0807.2137
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/164848
dc.subjectMetric Geometry
dc.subjectAlgebraic Geometry
dc.subject14P05; 52B11; 14Q99; 52A20
dc.titleThree-dimensional polyhedra can be described by three polynomial inequalities
dc.typetext

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