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Inner contact measures

Part of: General convexity

Published online by Cambridge University Press:  26 February 2010

WM. J. Firey
WM. J. Firey
Affiliation:
Oregon State University, Corvallis, Oregon, U.S.A.
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Extract

We say a motion g brings a mobile convex body K into inner contact with a fixed body K0 if the image gK lies in K0 and shares a boundary point with K0; we speak of the inner contact being at the common boundary point. The mobile body K is said to roll freely in K0 if, corresponding to each boundary point x of K0 and each rotation R, there is a translation t such that RK + t = gK has inner contact with K0 at x.

MSC classification

Secondary: 52A20: Convex sets in $n$ dimensions (including convex hypersurfaces)
Type
Research Article
Information
Mathematika , Volume 26 , Issue 1 , June 1979 , pp. 106 - 112
Copyright
Copyright © University College London 1979

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References

1.Blaschke, W.. Kreis und Kugel (Leipzig, 1916).CrossRefGoogle Scholar
2.Bonnesen, T. and Fenchel, W.. Theorie der konvexen Körper (Berlin, 1934).Google Scholar
3.Deltheil, R.. Probabilités géométriques (Paris, 1926).Google Scholar
4.Fenchel, W. and Jessen, B.. “Mengenfunktionen und konvexe Körper”, Danske Vid. Selskab Mat. -fys. Medd., 16(1938), 1–31.Google Scholar
5.Firey, W.. “Kinematic measures for sets of support figures”, Mathematika, 21 (1974), 270–281.CrossRefGoogle Scholar
6.Koutroufiotis, D.. “On Blaschke's rolling theorems”, Arch. Math., 23 (1972). 655–660.CrossRefGoogle Scholar
7.Santaló, L.. Integral geometry and geometric probability (Reading, Mass.-London-Amsterdam, 1976).Google Scholar
8.Schneider, R.. “Kinematische Berührmasse für konvexe Körper und Integralrelationen für Oberflächenmasse”, Math. Ann., 218 (1975), 253–267.CrossRefGoogle Scholar
9.Schneider, R.. “Kinematic measures for sets of colliding convex bodies”, Mathematika, 25 (1978). 1–12.CrossRefGoogle Scholar
10.Weil, W.. “Berührwahrscheinlichkeiten für konvexe Körper”, (to appear).Google Scholar