Bodies with similar projections

G. D. Chakerian, B. Lutwak

Research output: Contribution to journalArticle

Abstract

Aleksandrov's projection theorem characterizes centrally symmetric convex bodies by the measures of their orthogonal projections on lower dimensional subspaces. A general result proved here concerning the mixed volumes of projections of a collection of convex bodies has the following corollary. If K is a convex body in R" whose projections on r-dimensional subspaces have the same r-dimensional volume as the projections of a centrally symmetric convex body A/, then the Quermassintegrals satisfy \Vj(M) Wj(K), for 0 < j < n -r, with equality, for any j, if and only if K is a translate of M. The case where K is centrally symmetric gives Aleksandrov's projection theorem.

Original languageEnglish (US)
Pages (from-to)1811-1820
Number of pages10
JournalTransactions of the American Mathematical Society
Volume349
Issue number5
StatePublished - Dec 1 1997

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Keywords

  • Convex body
  • Generalized zonoid
  • Mixed volume
  • Quermassintegral
  • Relative brightness
  • Relative girth
  • Zonoid

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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