Geometriae Dedicata

, Volume 82, Issue 1, pp 285–323

Integral Geometry of Tame Sets

  • Ludwig Bröcker
  • Martin Kuppe

DOI: 10.1023/A:1005248711077

Cite this article as:
Bröcker, L. & Kuppe, M. Geometriae Dedicata (2000) 82: 285. doi:10.1023/A:1005248711077


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.

integral geometry tame stratifications 

Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • Ludwig Bröcker
    • 1
  • Martin Kuppe
    • 2
  1. 1.Mathematisches InstitutMünsterGermany
  2. 2.Mathematisches InstitutMünsterGermany

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