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arXiv · 0902.1414

Properties of distance functions on convex surfaces and applications

Jan Rataj·Ludek Zajicek
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Abstract

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 $X\times X$ in the only natural extrinsic sense. An analogous result holds for the squared distance function $\dist^2(x,F)$ from a closed set $F \subset X$. Applications concerning $r$-boundaries (distance spheres) and the ambiguous locus (exoskeleton) of a closed subset of a convex surface are given.

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Jan Rataj, Ludek Zajicek. 2009-11-20. Properties of distance functions on convex surfaces and applications. https://arxiv.org/abs/0902.1414

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