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Translative integral formulae for convex bodies

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Abstract

Translative versions of the principal kinematic formula for quermassintegrals of convex bodies are studied. The translation integral is shown to be a sum of Crofton type integrals of mixed volumes. As corollaries new integral formulas for mixed volumes are obtained. For smooth centrally symmetric bodies the functionals occurring in the principal translative formula are expressed by measures on Grassmannians which are related to the generating measures of the bodies.

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Authors and Affiliations

  1. Mathematics Department, Oklahoma University, 73019, Norman, OK, USA

    Paul Goodey & Wolfgang Weil

  2. Mathematisches Institut II, Universität Karlsruhe, Englerstrasse 2, D-7500, Karlsruhe, W. Germany

    Paul Goodey & Wolfgang Weil

Authors
  1. Paul Goodey
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  2. Wolfgang Weil
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Dedicated to Professor Otto Haupt with best wishes on his 100th birthday

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Goodey, P., Weil, W. Translative integral formulae for convex bodies. Aeq. Math. 34, 64–77 (1987). https://doi.org/10.1007/BF01840124

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  • DOI: https://doi.org/10.1007/BF01840124

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