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Integral geometry of pairs of planes

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Abstract

We deal with integrals of invariant measures of pairs of planes in the Euclidean space \({\mathbb {E}}^{3}\) 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.

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Authors and Affiliations

  1. Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193, Bellaterra, Barcelona, Catalonia, Spain

    Julià Cufí, Eduardo Gallego & Agustí Reventós

Authors
  1. Julià Cufí
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  2. Eduardo Gallego
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  3. Agustí Reventós
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Correspondence to Eduardo Gallego.

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The authors were partially supported by Grants 2017SGR358, 2017SGR1725 (Generalitat de Catalunya) and PGC2018-095998-B-100 (FEDER/MICINN)

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Cufí, J., Gallego, E. & Reventós, A. Integral geometry of pairs of planes. Arch. Math. 117, 579–591 (2021). https://doi.org/10.1007/s00013-021-01651-8

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  • DOI: https://doi.org/10.1007/s00013-021-01651-8

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