Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-23T04:55:09.155Z Has data issue: false hasContentIssue false
  • English
  • Français

Kinematic measures for sets of colliding convex Bodies

Part of: Global differential geometry General convexity Geometric probability and stochastic geometry

Published online by Cambridge University Press:  26 February 2010

Rolf Schneider
Rolf Schneider
Affiliation:
Albert-Ludwigs-Universität, Freiburg i. Br., Germany.
Get access

Extract

Consider two convex bodies K, K′ in Euclidean space En and paint subsets β, β′ on the boundaries of K and K′. Now assume that K′ undergoes random motion in such a way that it touches K.

MSC classification

Secondary: 52A20: Convex sets in $n$ dimensions (including convex hypersurfaces) 53C65: Integral geometry 60D05: Geometric probability and stochastic geometry
Type
Research Article
Information
Mathematika , Volume 25 , Issue 1 , June 1978 , pp. 1 - 12
Copyright
Copyright © University College London 1978

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Ewald, G., Larman, D. G. and Rogers, C. A.. “The directions of the line segments and of the r-dimensional balls on the boundary of a convex body in Euclidean space”, Mathematika, 17 (1970), 1–20.CrossRefGoogle Scholar
2.Federer, H.. “Curvature measures”. Trans. Amer. Math. Soc, 93 (1959), 418–191.Google Scholar
3.Federer, H.. Geometric measure theory (Springer, Berlin-Heidelberg-New York, 1969).Google Scholar
4.Firey, W. J.. “Kinematic measures for sets of support figures”, Mathematika, 21 (1974), 270–281.CrossRefGoogle Scholar
5.Flatto, L. and Newman, D. J.. “Random coverings”, Ada Math., 138 (1977), 241–264.Google Scholar
6.Goetz, A.. “Bemerkungen iiber Hausdorffsche MaBe und Hausdorffsche Dimensionen in Lieschen Gruppen”, Colloquium Math., 5 (1958), 55–65.CrossRefGoogle Scholar
7.Hadwiger, H.. Vorlesungen iiber Inhalt, Oberfliiche und Isoperimetrie (Springer, Berlin-Gottingen-Heidelberg, 1957).Google Scholar
8.McMullen, P.. “A dice probability problem”, Mathematika, 21 (1974), 193–198.Google Scholar
9.Schneider, R.. “Kinematische BeriihrmaBe für konvexe Korper und Integralrelationen fur Oberflachenma Be”, Math. Ann., 218 (1975), 253–267.CrossRefGoogle Scholar
10.Schneider, R.. “Eine kinematische Integralformel für konvexe Korper”, Arch. Math., 28 (1977), 217–220.CrossRefGoogle Scholar
11.Schneider, R.. “Curvature measures of convex bodies”, Ann. Mat. Pura Appl. (to appear).Google Scholar