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Identifying Set Inclusion by Projective Positions and Mixed Volumes

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Part of the Lecture Notes in Mathematics book series (LNM,volume 2116)

Abstract

We study a few approaches to identify inclusion (up to a shift) between two convex bodies in \(\mathbb{R}^{n}\). To this goal we use mixed volumes and fractional linear maps. We prove that inclusion may be identified by comparing volume or surface area of all projective positions of the sets. We prove similar results for Minkowski sums of the sets.

Keywords

  • Convex Body
  • Dimensional Subspace
  • Symmetric Case
  • Mixed Volume
  • European Research Council

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Notes

  1. 1.

    D.I. Florentin was partially supported by European Research Council grand Dimension 305629.

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Correspondence to Vitali Milman .

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Florentin, D., Milman, V., Segal, A. (2014). Identifying Set Inclusion by Projective Positions and Mixed Volumes. In: Klartag, B., Milman, E. (eds) Geometric Aspects of Functional Analysis. Lecture Notes in Mathematics, vol 2116. Springer, Cham. https://doi.org/10.1007/978-3-319-09477-9_11

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