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A local Steiner–type formula for general closed sets and applications

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Abstract.

We introduce support (curvature) measures of an arbitrary closed set A in ℝd and establish a local Steiner–type formula for the localized parallel volume of A. We derive some of the basic properties of these support measures and explore how they are related to the curvature measures available in the literature. Then we use the support measures in analysing contact distributions of stationary random closed sets, with a particular emphasis on the Boolean model with general compact particles.

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Authors and Affiliations

  1. Mathematisches Institut, Albert-Ludwigs-Universität, Eckerstr. 1, 79104, Freiburg i. Br., Germany

    Daniel Hug

  2. Institut für Mathematische Stochastik, Universität Karlsruhe (TH), Englerstr. 2, 76128, Karlsruhe, Germany

    Günter Last

  3. Mathematisches Institut II, Universität Karlsruhe (TH), Englerstr. 2, 76128, Karlsruhe, Germany

    Wolfgang Weil

Authors
  1. Daniel Hug
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  2. Günter Last
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  3. Wolfgang Weil
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Correspondence to Daniel Hug.

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Mathematics Subject Classification (2000): 53C65, 28A75, 52A22, 60D05; 52A20, 60G57, 60G55, 28A80.

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Hug, D., Last, G. & Weil, W. A local Steiner–type formula for general closed sets and applications. Math. Z. 246, 237–272 (2004). https://doi.org/10.1007/s00209-003-0597-9

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  • DOI: https://doi.org/10.1007/s00209-003-0597-9

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