Properties of distance functions on convex surfaces and applications

Details Properties of distance functions on convex surfaces and applications Properties of distance functions on convex surfaces and applications

2009-02-09

arxiv.org/abs/0902.1414v3

Mathematics

Metric Geometry

21 pages. Section 4. Applications was revised and improved

Scientific paper

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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