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Integral Geometry of Tame Sets

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Abstract

Curvature measures on certain tame Whitney-stratified sets are defined as coefficients of modified volume-growth polynomials. Stratified Morse theory yields alternative descriptions of these curvature measures for tame (possibly highly singular) sets. From this we obtain a generalized Gauss–Bonnet formula and various kinematic formulas. Finally, for O-minimal sets it is shown that curvature measures only depend on the inner metric.

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Authors and Affiliations

  1. Mathematisches Institut, Einsteinstrasse 62, D-48149, Münster, Germany

    Ludwig Bröcker

  2. Mathematisches Institut, Einsteinstrasse 62, D-48149, Münster, Germany

    Martin Kuppe

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  1. Ludwig Bröcker
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  2. Martin Kuppe
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Bröcker, L., Kuppe, M. Integral Geometry of Tame Sets. Geometriae Dedicata 82, 285–323 (2000). https://doi.org/10.1023/A:1005248711077

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