Steiner-Minkowski Polynomials of Convex Sets in High Dimension, and Limit Entire Functions

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dc.creatorKatsnelson, Victor
dc.date2007-09-01
dc.date.accessioned2026-07-07T08:27:07Z
dc.date.available2026-07-07T08:27:07Z
dc.descriptionFor a convex set (K) of the (n)-dimensional Euclidean space, the Steiner-Minkowski polynomial (M_K(t)) is defined as the (n)-dimensional Euclidean volume of the neighborhood of the radius (t). Being defined for positive (t), the Steiner-Minkowski polynomials are considered for all complex (t). The renormalization procedure for Steiner polynomial is proposed. The renormalized Steiner-Minkowski polynomials corresponding to all possible solid convex sets in all dimensions form a normal family in the whole complex plane. For each of the four families of convex sets: the Euclidean balls, the cubes, the regular cross-polytopes and the regular symplexes of dimensions (n), the limiting entire functions, as (n) tends to infinity, are calculated explicitly.
dc.description15 pages
dc.identifierhttps://arxiv.org/abs/0709.0037
dc.identifierhttp://arxiv.org/abs/0709.0037
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/137169
dc.subjectComplex Variables
dc.subjectMetric Geometry
dc.subject30-xx (Primary); 51 (Secondary)
dc.titleSteiner-Minkowski Polynomials of Convex Sets in High Dimension, and Limit Entire Functions
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