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Inner contact probabilities for convex bodies

Published online by Cambridge University Press:  01 July 2016

Wolfgang Weil
Wolfgang Weil*
Affiliation:
Universität Karlsruhe
*
∗Postal address: Mathematisches Institut II, Universität Karlsruhe, Englerstrasse 2, 7500 Karlsruhe 1, West Germany.
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Abstract

Let K and L be convex bodies in where L can roll freely in K. Suppose that Borel sets are painted in the boundaries of K and L. The probability that after a random rolling of L in K the contact is paint-to-paint is determined and expressed by curvature measures of K and L.

Keywords

CONTACT PROBABILITYCONVEX BODIESCURVATURE MEASURESKINEMATIC INTEGRAL FORMULA
Type
Research Article
Information
Advances in Applied Probability , Volume 14 , Issue 3 , September 1982 , pp. 582 - 599
Copyright
Copyright © Applied Probability Trust 1982 

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References

Blaschke, W. (1916) Kreis und Kugel. Veit & Co, Leipzig.Google Scholar
Firey, W. J. (1974) Kinematic measures for sets of support figures. Mathematika 21, 270–281.Google Scholar
Firey, W. J. (1979) Inner contact measures. Mathematika 26, 106–112.Google Scholar
Goodey, P. R. (1982) Connectivity and freely rolling bodies.Google Scholar
Matheron, G. (1975) Random Sets and Integral Geometry. Wiley, New York.Google Scholar
Matheron, G. (1978) La formule de Steiner pour les érosions. J. Appl. Prob. 15, 126–135.CrossRefGoogle Scholar
McMullen, P. (1974) A dice probability problem. Mathematika 21, 193–198.Google Scholar
Miles, R. E. (1974) On the elimination of edge effects in planar sampling. In Stochastic Geometry, ed. Harding, E. F. and Kendall, D. G., Wiley, London, 228–247.Google Scholar
Neveu, J. (1977) Processus ponctuels. In Lecture Notes in Mathematics 598, Springer-Verlag, Berlin, 249–447.Google Scholar
Schneider, R. (1978a) Curvature measures of convex bodies. Ann. Mat. Pura Appl. 116, 101–134.Google Scholar
Schneider, R. (1978b) Kinematic measures for sets of colliding convex bodies. Mathematika 25, 1–12.Google Scholar
Weil, W. (1973) Ein Approximationssatz für konvexe Körper. Manuscripta Math. 8, 335–362.Google Scholar
Weil, W. (1974) über den Vektorraum der Differenzen von Stützfunktionen konvexer Körper. Math. Nachr. 59, 353–369.CrossRefGoogle Scholar
Weil, W. (1979a) Berührwahrscheinlichkeiten für konvexe Körper. Z. Wahrscheinlichkeitsth. 48, 327–338.Google Scholar
Weil, W. (1979b) Kinematic integral formulas for convex bodies. In Contributions to Geometry, ed. Tölke, J. and Wills, J. M., Birkhäuser, Basel, 60–76.Google Scholar
Weil, W. (1980) Eine Charakterisierung von Summanden konvexer Körper. Arch. Math. 34, 283–288.Google Scholar