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Properties of distance functions on convex surfaces and applications

Jan Rataj, Luděk Zajíček (2011)

Czechoslovak Mathematical Journal

If X is a convex surface in a Euclidean space, then the squared intrinsic distance function dist 2 ( x , y ) is DC (d.c., delta-convex) on X × X in the only natural extrinsic sense. An analogous result holds for the squared distance function dist 2 ( x , F ) from a closed set F X . Applications concerning r -boundaries (distance spheres) and ambiguous loci (exoskeletons) of closed subsets of a convex surface are given.

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