A kinematic formula for the total absolute curvature of intersections

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Given two surfaces in three dimensional euclidean space, one fixed and the other moved by rigid motions, we consider the total absolute curvature of the intersection curves. In this paper we investigate the integral of these total absolute curvatures over all motions. Under some geometric conditions we obtain kinematic formulas, and with weaker conditions we get upper and lower bounds. Finally, as applications, we obtain upper bounds for the average number of connected components of the intersections, and we give Hadwiger conditions for a convex domain to be able to contain another one. © 2010 de Gruyter.
Original languageEnglish
Pages (from-to)709-718
JournalAdvances in Geometry
Publication statusPublished - 1 Oct 2010


  • Integral geometry
  • Kinematic formulas
  • Total absolute curvature


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