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In this chapter, we consider identities of the form \(\displaystyle \int _{G(n,k)}\varphi _L(K\cap L)\,\nu _k(\mathrm{d} L)=\varphi (K) {} \) for tensor-valued functionals. We focus on the case where either \(\varphi _L\) or \(\varphi \) is a Minkowski tensorRotational Crofton formulafor Minkowski tensors.

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Rotational Crofton Formulae for Minkowski Tensors

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  • 发表日期：

    2025年

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  • Eva B. Vedel Jensen,
  • Markus Kiderlen

摘要

In this chapter, we consider identities of the form \(\displaystyle \int _{G(n,k)}\varphi _L(K\cap L)\,\nu _k(\mathrm{d} L)=\varphi (K) {} \) for tensor-valued functionals. We focus on the case where either \(\varphi _L\) or \(\varphi \) is a Minkowski tensorRotational Crofton formulafor Minkowski tensors.