Integral geometry of pairs of planes

Julià Cufí, Eduardo Gallego*, Agustí Reventós

*Corresponding author for this work

Research output: Contribution to journalArticleResearchpeer-review

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We deal with integrals of invariant measures of pairs of planes in the Euclidean space E3 as considered by Hug and Schneider. In this paper, we express some of these integrals in terms of functions of the visual angle of a convex set. As a consequence of our results, we evaluate the deficit in a Crofton-type inequality due to Blaschke.

Original languageEnglish
Pages (from-to)579-591
Number of pages13
JournalArchiv der Mathematik
Issue number5
Publication statusPublished - 1 Nov 2021


  • Constant width
  • Convex set
  • Invariant measure
  • Visual angle


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