Singularities of virtual polytopes

Martinez‐Maure, Yves; Panina, Gaiane

doi:10.1007/s00022-014-0211-9

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2016

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“…Virtual polytopes, which are the corresponding objects with K n replaced by the set P n of convex polytopes in R n , were introduced and studied by Pukhlikov and Khovanskii [9]. A recent contribution is by Martinez-Maure and Panina [7]. The survey on virtual polytopes by Panina and Streinu [8] describes a number of 'geometrizations' of virtual polytopes and their applications.…”

Section: Introductionmentioning

confidence: 99%

The typical irregularity of virtual convex bodies

Schneider

2016

Preprint

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The semigroup of convex bodies in R n with Minkowski addition has a canonical embedding into an abelian group; its elements have been called virtual convex bodies. Geometric interpretations of such virtual convex bodies have been particularly fruitful under the restriction to polytopes. For general convex bodies, mainly the planar case has been studied, as a part of the more general investigation of hedgehogs. Here we restrict ourselves to strictly convex bodies in R n . A particularly natural geometric interpretation of virtual convex bodies can then be seen in the set of differences of boundary points of two convex bodies with the same outer normal vector. We describe how in the typical case (in the sense of Baire category) this leads to a highly singular object.

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Section: Introductionmentioning

confidence: 99%

The typical irregularity of virtual convex bodies

Schneider

2016

Preprint

View full text Add to dashboard Cite

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Singularities of virtual polytopes

Cited by 1 publication

References 7 publications

The typical irregularity of virtual convex bodies

The typical irregularity of virtual convex bodies

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