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Connectivity and freely rolling convex bodies

Part of: General convexity

Published online by Cambridge University Press:  26 February 2010

P. R. Goodey
P. R. Goodey
Affiliation:
Mathematics Department, Royal Holloway College, Englefield Green, Surrey.
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Abstract

If C and Co are two convex bodies in Ed we say that C slides (rolls) freely inside Co if the following condition is satisfied: for each x ∈ ∂C0 (and each rotation R) there is a translation t such that, if gC = C + t (= RC + t), then gC ⊂ Co and x ∈ ∂gC. This work establishes certain topological conditions which ensure the free rolling and sliding of C inside Co. One consequence of these conditions is that, if ∂K ∩ int gK is a topological ball for all rigid motions g, then K is a ball in the geometrical sense.

MSC classification

Secondary: 52A20: Convex sets in $n$ dimensions (including convex hypersurfaces)
Type
Research Article
Information
Mathematika , Volume 29 , Issue 2 , December 1982 , pp. 249 - 259
Copyright
Copyright © University College London 1982

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