Intersections of Convex Bodies with Their Translates

P. R. Goodey and M. M. Woodcock
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P. R. Goodey: Royal Holloway College, Mathematics Department
M. M. Woodcock: Royal Holloway College, Mathematics Department

A chapter in The Geometric Vein, 1981, pp 289-296 from Springer

Abstract: Abstract It has been shown by Fujiwara [4] and Bol [2] that if K is a planar convex body which is not a disk, then it is possible to find a congruent copy K′ of K such that K and K′ have more than two points in common on their boundaries. This result was used by Yanagihara [9] to show that if K is a 3-dimensional convex body with the property that for any congruent copy K′ of K, the boundaries of K and K′ intersect in a planar curve (assuming they do, in fact, meet but do not coincide), then K is a ball.

Keywords: Convex Body; Support Function; Boundary Component; Planar Curve; Constant Width (search for similar items in EconPapers)
Date: 1981
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DOI: 10.1007/978-1-4612-5648-9_21

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