Sharp affine stability estimates for Hammer's problem

Carla Peri, Paolo Dulio, Marco Longinetti, Adriana Venturi

Risultato della ricerca: Contributo in rivistaArticolo in rivistapeer review

2 Citazioni (Scopus)

Abstract

We prove that the area distance between two convex bodies K and K' with the same parallel X-rays in a set of n mutually non parallel directions is bounded from above by the area of their intersection, times a constant depending only on n. Equality holds if and only if K is a regular n-gon, and K' is K rotated by π/n about its center, up to affine transformations. This and similar sharp affine invariant inequalities lead to stability estimates for Hammer’s problem if the n directions are known up to an error, or in case X-rays emanating from n collinear points are considered. For n = 4, the order of these estimates is compared with the cross ratio of given directions and given points, respectively.
Lingua originaleEnglish
pagine (da-a)27-51
Numero di pagine25
RivistaAdvances in Applied Mathematics
Volume41
DOI
Stato di pubblicazionePubblicato - 2008

Keywords

  • Hammer's problem
  • X-ray
  • affinely regular polygon
  • stability

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