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PROPERTIES OF DISTANCE FUNCTIONS ON CONVEX SURFACES AND APPLICATIONS
, 902
"... 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., deltaconvex) 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 ..."
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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., deltaconvex) 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 rboundaries (distance spheres) and the ambiguous locus (exoskeleton) of a closed subset of a convex surface are given. 1.